2024/05/21 by Maxime Murray, Murray, Maxime, J. D. Mireles James +1
Agricultural and Biological Sciences · Engineering · Mathematics · #Advanced Scientific Research Methods #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematics and Applications #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2405.12446
openalex publication_date 2024/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work develops a functional analytic framework for making computer assisted arguments involving transverse heteroclinic connecting orbits between hyperbolic periodic solutions of ordinary differential equations. We exploit a Fourier-Taylor approximation of the local stable/unstable manifold of the periodic orbit, combined with a numerical method for solving two point boundary value problems via Chebyshev series approximations. The a-posteriori analysis developed provides mathematically rigorous bounds on all approximation errors, providing both abstract existence results and quantitative information about the true heteroclinic solution. Example calculations are given for both the dissipative Lorenz system and the Hamiltonian Hill Restricted Four Body Problem.