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Computation of maximal local (un)stable manifold patches by the parameterization method
M. Breden, J.-P. Lessard and J.D. Mireles James.
Indagationes Mathematicae, 27(1): 340–367, 2016
PDF arXiv:1508.02615 doi:10.1016/j.indag.2015.11.001 Publication [25]
Files
Codes and data accompanying the paper, reproducing the computer-assisted proofs it reports.
- maximizing_manifold.zip (78 KB)
Codes/ — 87 files (72 KB)
- Bridge/DF.m (413 B)
- Bridge/Dg_lin.m (293 B)
- Bridge/Dg_nonlin.m (624 B)
- Bridge/F.m (507 B)
- Bridge/M_alpha.m (244 B)
- Bridge/Newton.m (336 B)
- Bridge/V_alpha_1.m (198 B)
- Bridge/V_alpha_2.m (194 B)
- Bridge/Y.m (198 B)
- Bridge/Z0.m (96 B)
- Bridge/Z1.m (240 B)
- Bridge/Z2.m (188 B)
- Bridge/cauchy.m (396 B)
- Bridge/cauchy_fft.m (978 B)
- Bridge/compute_AF.m (640 B)
- Bridge/eval_parameterization.m (618 B)
- Bridge/find_column.m (222 B)
- Bridge/g_lin.m (124 B)
- Bridge/multiple.m (161 B)
- Bridge/norm_1D.m (383 B)
- Bridge/norm_multiD.m (285 B)
- Bridge/norm_op.m (281 B)
- Bridge/position.m (205 B)
- Bridge/proof.m (546 B)
- Bridge/proof_max_r.m (1.5 KB)
- Bridge/rescale.m (561 B)
- Bridge/scriptBridgeProof.m (2.6 KB)
- Bridge/triangulate_complex.m (1.4 KB)
- Bridge/vect2mat.m (581 B)
- FHN/DF.m (379 B)
- FHN/Dg_lin.m (332 B)
- FHN/Dg_nonlin.m (649 B)
- FHN/F.m (557 B)
- FHN/V_alpha_1.m (198 B)
- FHN/V_alpha_2.m (194 B)
- FHN/cauchy.m (396 B)
- FHN/cauchy_fft.m (978 B)
- FHN/coef_F.m (739 B)
- FHN/compute_para_fast_slow.m (4.5 KB)
- FHN/compute_para_max_surface_area.m (5.9 KB)
- FHN/defect.m (330 B)
- FHN/eval_para_vectorialized.m (465 B)
- FHN/eval_parameterization.m (618 B)
- FHN/find_column.m (225 B)
- FHN/g_lin.m (181 B)
- FHN/multiple.m (164 B)
- FHN/norm_1D.m (383 B)
- FHN/norm_multiD.m (285 B)
- FHN/partial_derivative.m (573 B)
- FHN/position.m (204 B)
- FHN/prod_vect.m (391 B)
- FHN/scriptFHNMax.m (928 B)
- FHN/scriptFHNRatio.m (1.1 KB)
- FHN/surface_value.m (848 B)
- FHN/triangulate.m (1.4 KB)
- FHN/triangulate_complex.m (1.5 KB)
- FHN/vect2mat.m (516 B)
- Lorenz/DF.m (332 B)
- Lorenz/Dg_lin.m (264 B)
- Lorenz/Dg_nonlin.m (827 B)
- Lorenz/F.m (518 B)
- Lorenz/V_alpha_1.m (198 B)
- Lorenz/V_alpha_2.m (194 B)
- Lorenz/cauchy.m (396 B)
- Lorenz/cauchy_fft.m (978 B)
- Lorenz/coef_F.m (1002 B)
- Lorenz/compute_para_Lorenz.m (6.6 KB)
- Lorenz/compute_para_Lorenz_max.m (5.7 KB)
- Lorenz/compute_para_Lorenz_ratio.m (3.9 KB)
- Lorenz/defect.m (330 B)
- Lorenz/eval_para_vectorialized.m (465 B)
- Lorenz/eval_parameterization.m (618 B)
- Lorenz/find_column.m (222 B)
- Lorenz/g_lin.m (134 B)
- Lorenz/lorenzField.m (183 B)
- Lorenz/multiple.m (161 B)
- Lorenz/norm_1D.m (383 B)
- Lorenz/norm_multiD.m (285 B)
- Lorenz/partial_derivative.m (573 B)
- Lorenz/position.m (205 B)
- Lorenz/prod_vect.m (391 B)
- Lorenz/scriptLorenzAll.m (2.1 KB)
- Lorenz/scriptLorenzRatio.m (1.2 KB)
- Lorenz/surface_value.m (848 B)
- Lorenz/triangulate.m (1.4 KB)
- Lorenz/triangulate_complex.m (1.5 KB)
- Lorenz/vect2mat.m (516 B)
The scripts are written in MATLAB; the rigorous parts require the interval arithmetic package INTLAB to be installed and started.