update

Source/TODEL_area.py

@@ -1,67 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-import potentials as pot
-import integrator as itg
-import initial_conditions as init
-
-# Parameters
-h = 0.01  # Step size for integrator
-N_inter = 500 # Number of iterations for distance calculation
-eps = 1e-3  # Perturbation distance
-mu_c = 0.6  # Threshold for classifying ergodic vs regular
-energy_values = np.array([0.01, 0.02, 0.04, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18])
-N_PART = 100
-
-def classify_point(P1, P1_prime):
-    pos_t1, positions1 = itg.rk4(0, P1, h, N_inter, pot.hh_evolution)
-    pos_t2, positions2 = itg.rk4(0, P1_prime, h, N_inter, pot.hh_evolution)
-
-    # Compute the sum of squared distances (μ)
-    mu = 0
-    for i in range(N_inter):
-        y1, y_dot1 = positions1[i, 0, 1], positions1[i, 1, 1]
-        y2, y_dot2 = positions2[i, 0, 1], positions2[i, 1, 1]
-        x1, x_dot1 = positions1[i, 0, 0], positions1[i, 1, 0]
-        x2, x_dot2 = positions2[i, 0, 0], positions2[i, 1, 0]
-
-        squared_distance = (np.sqrt((x2 - x1)**2 + (y2 - y1) ** 2 + (x_dot2 - x_dot1) ** 2 +(y_dot2 - y_dot1) ** 2))**2
-        mu += squared_distance
-
-    return mu
-
-# Analyze for different energy values
-relative_areas = []
-
-for E in energy_values:
-    # Generate initial conditions for the given energy level
-    initial_conditions = init.n_energy_part(pot.hh_potential, N=N_PART, E=E)
-    initial_conditions_eps = initial_conditions.copy()
-    initial_conditions_eps[0,1] += eps
-    n_regular = 0
-
-    # Loop through each initial condition
-    for i in range(N_PART):
-        P1 = initial_conditions[:, :, i]
-        # Perturb the initial point slightly
-        P1_prime = initial_conditions_eps[:,:,i]
-
-        # Classify the point based on the evolution
-        mu = classify_point(P1, P1_prime)
-        np.nan_to_num(mu, copy=False, nan=1.0)
-
-        print(f"the mu value is {mu}")
-        if mu < mu_c:
-            n_regular += 1
-
-    # Compute the relative area covered by regular points
-    relative_area = n_regular / N_PART
-    relative_areas.append(relative_area)
-
-# Plot the results
-plt.figure()
-plt.plot(energy_values, relative_areas, marker='o', color='C0')
-plt.xlabel("Energy (E)")
-plt.ylabel("Relative Area Covered by Regular Curves")
-plt.title("Transition from Ergodic to Stable Regime")
-plt.grid()
-plt.show()

Source/TODEL_equations.py

@@ -1,17 +0,0 @@
-from sympy import *
-
-# Forces
-X, Y, U, V = symbols("X, Y, U, V")
-POT = (X**2 + Y**2 + 2*X**2*Y - 2*Y**3/3)/2
-KIN = (U**2 + V**2)/2
-TOT = KIN + POT
-
-DX = diff(POT, X)
-DY = diff(POT, Y)
-
-FX = -DX
-FY = -DY
-
-print(FX)
-print(FY)
-

Source/TODEL_main_yael.py

@@ -1,114 +0,0 @@
-import time
-import numpy as np
-import matplotlib.pyplot as plt
-from scipy.optimize import curve_fit
-
-import potentials as pot
-import energies as ene
-import integrator as itg
-import initial_conditions as init
-import poincare_sections as pcs
-
-if "YII_light_1" in plt.style.available: 
-    plt.style.use("YII_light_1")
-# Loading matplotlib style...
-# PARAM
-N_grid = 1000
-N_inter = int(1e5)
-N_part = 200
-#all_E = np.array([1/100, 1/12, 1/10, 1/8, 1/6])
-all_E = np.linspace(1/100, 1/6, 20)
-h = 0.005
-
-mu_c = 1e-4
-d_12 = 1e-7
-
-# INIT
-W_grid = init.mesh_grid(N_grid, xmin=-1, xmax=1, ymin=-1, ymax=1)
-X_grid = W_grid[0]
-Y_grid = W_grid[1]
-potential = pot.hh_potential(W_grid, position_only=True)
-
-# MAIN
-def gen_mu(E):
-    pot_valid = np.ma.masked_where(potential > E, potential)
-    W_1 = init.n_energy_part(pot.hh_potential, N_part, E)
-    W_2 = np.zeros_like(W_1)
-    alpha = np.random.uniform(0, 2*np.pi, N_part)
-    W_2[0, 0] = W_1[0, 0] + d_12*np.cos(alpha)
-    W_2[0, 1] = W_1[0, 1] + d_12*np.sin(alpha)
-    W_2[1, 0] = W_1[1, 0]
-    W_2[1, 1] = W_1[1, 1]
-
-    t_1, positions_1 = itg.rk4(0, W_1, h, N_inter, pot.hh_evolution)
-    x_1 = positions_1[:, 0, 0]
-    y_1 = positions_1[:, 0, 1]
-    u_1 = positions_1[:, 1, 0]
-    v_1 = positions_1[:, 1, 1]
-    
-    t_2, positions_2 = itg.rk4(0, W_2, h, N_inter, pot.hh_evolution)
-    x_2 = positions_2[:, 0, 0]
-    y_2 = positions_2[:, 0, 1]
-    u_2 = positions_2[:, 1, 0]
-    v_2 = positions_2[:, 1, 1]
-    dist_sq = (x_2[-25:] - x_1[-25:])**2 \
-            + (y_2[-25:] - y_1[-25:])**2 \
-            + (u_2[-25:] - u_1[-25:])**2 \
-            + (v_2[-25:] - v_1[-25:])**2
-
-    mu = np.sum(dist_sq, axis=0)
-    return mu
-
-A = np.zeros_like(all_E)
-MU = []
-ALL_E = []
-for i in range(len(all_E)):
-    mu = gen_mu(all_E[i])
-    n_total = N_part
-    n_ergo = np.sum(mu < mu_c) # count how many times the condition is verified
-    A[i] = n_ergo/n_total
-    MU.append(mu)
-    ALL_E.append([all_E[i]]*len(mu))
-
-MU = np.array(MU)
-ALL_E = np.array(ALL_E)
-
-# def lin(x, a, b):
-#     return a*x + b
-
-# w_chaos = np.argwhere(A < 1).flatten()
-# X = all_E[w_chaos]
-# Y = A[w_chaos]
-
-# popt, pcov = curve_fit(lin, X, Y)
-# a, b = popt
-# da, db = np.sqrt(np.diag(pcov))
-
-fig, ax = plt.subplots(1)
-ax.scatter(ALL_E, MU, s=1, 
-           color="k", alpha=0.1, label="Data")
-ax.scatter(all_E, np.mean(MU, axis=1), s=10, 
-           color="C3", marker="*", label="Mean")
-ax.scatter(all_E, np.median(MU, axis=1), s=10, 
-           color="C2", marker="s", label="Median")
-ax.hlines(mu_c, np.min(all_E), np.max(all_E), color="C4")
-ax.legend()
-ax.set_yscale("log")
-ax.set_xlabel("energy E")
-ax.set_ylabel("quantity mu")
-
-fig.tight_layout()
-# fig.savefig("mu")
-
-fig, ax = plt.subplots(1)
-ax.scatter(all_E, A, color="C0", s=5, marker="o", label="Data")
-ax.set_xlabel("energy E")
-ax.set_ylabel("area A")
-ax.legend()
-fig.tight_layout()
-# fig.savefig("area")
-plt.show()
-
-
-
-    

Source/TODEL_poincare_test.py

@@ -1,58 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-import potentials as pot
-import energies as ene
-import integrator as itg
-import initial_conditions as init
-import poincare_sections as pcs
-
-h = 0.01
-N_inter = 30000
-eps = 1e-2
-
-x_0 = 0.0
-y_vals = np.linspace(0, 0.6, 50)
-E = 0.125  # 1/12
-
-# Initialize lists to store all Poincaré points across different initial conditions
-all_pcs_pos_y = []
-all_pcs_vel_y = []
-
-
-for i in range(len(y_vals)):
-    y0 = y_vals[i]
-    W_part = init.one_part(x_0, y0, 0, 0)
-    POT = pot.hh_potential(W_part)[0]
-    u_0 = np.sqrt(2 * (E - POT))
-    v_0 = 0.0
-
-
-    W_part[1, 0] = u_0
-    W_part[1, 1] = v_0
-
-    # Perform integration
-    pos_t, positions = itg.rk4(0, W_part, h, N_inter, pot.hh_evolution)
-
-    # Extract positions and velocities
-    pos_x = positions[:, 0, 0]
-    pos_y = positions[:, 0, 1]
-    vel_x = positions[:, 1, 0]
-    vel_y = positions[:, 1, 1]
-
-    # Find Poincaré section points for the current initial condition
-    pcs_pos_y, pcs_vel_y = pcs.pcs_find(pos_x, pos_y, vel_x, vel_y)
-
-    # Append the current Poincaré section points to the overall lists
-    all_pcs_pos_y.extend(pcs_pos_y)
-    all_pcs_vel_y.extend(pcs_vel_y)
-
-# Plotting all Poincaré section points on the same graph
-fig, ax = plt.subplots()
-ax.scatter(all_pcs_pos_y, all_pcs_vel_y, s=2, color="C4")
-
-# Set labels and legend
-ax.set_xlabel("coordinate y")
-ax.set_ylabel("velocity v")
-ax.set_title("Combined Poincaré Section for Multiple Initial y0 Values")
-
-plt.show()

Source/YII_1.mplstyle

@@ -1,3 +1,29 @@
+#@ Author: Moussouni, Yaël (MSc student)
+#@ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
+#                de Strasbourg, UMR 7550, F-67000 Strasbourg, France
+#@ Date: 2025-01-01
+#
+#Licence:
+#Order and Chaos in a 2D potential
+#Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+#                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+#
+#YII_1.mplstyle
+#Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+#
+#This program is free software: you can redistribute it and/or modify
+#it under the terms of the GNU General Public License as published by
+#the Free Software Foundation; either version 3 of the License, or
+#(at your option) any later version.
+#
+#This program is distributed in the hope that it will be useful,
+#but WITHOUT ANY WARRANTY; without even the implied warranty of
+#MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+#GNU General Public License for more details.
+#
+#You should have received a copy of the GNU General Public License
+#along with this program. If not, see https://www.gnu.org/licenses/.
+
 ### Axes
 axes.titlesize : large
 axes.labelsize : large

Source/YII_light_1.mplstyle

@@ -1,3 +1,29 @@
+#@ Author: Moussouni, Yaël (MSc student)
+#@ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
+#                de Strasbourg, UMR 7550, F-67000 Strasbourg, France
+#@ Date: 2025-01-01
+#
+#Licence:
+#Order and Chaos in a 2D potential
+#Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+#                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+#
+#YII_light_1.mplstyle
+#Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+#
+#This program is free software: you can redistribute it and/or modify
+#it under the terms of the GNU General Public License as published by
+#the Free Software Foundation; either version 3 of the License, or
+#(at your option) any later version.
+#
+#This program is distributed in the hope that it will be useful,
+#but WITHOUT ANY WARRANTY; without even the implied warranty of
+#MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+#GNU General Public License for more details.
+#
+#You should have received a copy of the GNU General Public License
+#along with this program. If not, see https://www.gnu.org/licenses/.
+
 ### Axes
 axes.titlesize : large
 axes.labelsize : large

Source/energies.py

@@ -7,7 +7,29 @@ Compute energies (kinetic or total)
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-12-13
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+energies.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
 """
 
 import numpy as np

Source/initial_conditions.py

@@ -7,7 +7,29 @@ Generate initial conditions depending on different criteria
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+initial_conditions.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
 """
 
 import numpy as np

Source/integrator.py

@@ -7,7 +7,30 @@ Integrate differential equations.
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+integrator.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
+
 """
 import numpy as np
 

Source/main_area.py

@@ -8,7 +8,30 @@ study ordered and chaotic regimes.
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-12-13
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+main_area.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
+
 """
 import numpy as np
 from scipy.optimize import curve_fit

Source/main_poincare_sections_linear.py

@@ -8,7 +8,30 @@ Computes the Poincaré Sections with a linear algorithm
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+main_poincare_sections_linear.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
+
 """
 import numpy as np
 

Source/main_poincare_sections_parallel.py

@@ -7,7 +7,30 @@ Computes the Poincaré Sections with a parallel algorithm (with Numpy)
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+main_poincare_sections_parallel.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
+
 """
 import numpy as np
 

Source/plot_area.py

@@ -7,7 +7,30 @@ Plots areas
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+plot_area.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
+
 """
 import os
 import numpy as np

Source/plot_poincare_sections.py

@@ -8,7 +8,30 @@ or parallel algorithms.
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+plot_poincare_sections.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
+
 """
 import os
 import numpy as np

Source/plot_poincare_sections_zoom.py

@@ -8,7 +8,29 @@ or parallel algorithms.
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+plot_poincare_sections_zoom.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
 """
 import os
 import numpy as np

Source/poincare_sections.py

@@ -7,7 +7,29 @@ Computes the Poincaré Sections
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+poincare_sections.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
 """
 
 import numpy as np

Source/potentials.py

@@ -7,7 +7,30 @@ Functions of the different potentials (and their derivatives for the evolution)
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+potentials.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
+
 """
 
 import numpy as np

Source/test_evolution.py

@@ -8,7 +8,30 @@ followed by the particle in a given time.
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+test_evolution.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
+
 """
 
 import numpy as np

Source/test_initial_E.py

@@ -7,7 +7,30 @@ Sample random particles with the same given energy in a valid coordinates range.
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+test_initial_E.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
+
 """
 import numpy as np
 import matplotlib.pyplot as plt

Source/test_potentials.py

@@ -7,7 +7,30 @@ Draw the Kepler potential and the Hénon--Heils potential
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+test_potentials.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
+
 """
 import numpy as np
 import matplotlib.pyplot as plt

Source/time_poincare_sections.py

@@ -7,7 +7,29 @@ Computes the running time between the linear and parallel algorithms.
 @ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student)
 @ Institution:  Université de Strasbourg, CNRS, Observatoire astronomique
                 de Strasbourg, UMR 7550, F-67000 Strasbourg, France
-@ Date: 2024-11-29
+@ Date: 2025-01-01
+
+Licence:
+Order and Chaos in a 2D potential
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+time_poincare_sections.py
+Copyright (C) 2025 Yaël Moussouni (yael.moussouni@etu.unistra.fr)
+                   Bhat, Junaid Ramzan (junaid-ramzan.bhat@etu.unistra.fr)
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see https://www.gnu.org/licenses/.
 """
 
 import time