2019/03/04 by Irmina Walawska, Daniel Wilczak · 11 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Artificial intelligence #Bifurcation #Computer science #Control theory (sociology) #Geometry #Halo #Hamiltonian (control theory) #Hamiltonian system #Lyapunov function #Mathematical analysis #Mathematical optimization #Mathematics #Nonlinear system #Nuclear physics research studies #Period (music) #Periodic orbits #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Symmetry (geometry) #math.DS #msc:37C27 #msc:37M20 #msc:65G20 #msc:65P30
paper · pdf · doi:10.1016/j.cnsns.2019.03.005
published in Communications in Nonlinear Science and Numerical Simulation 74, 30-54 (Elsevier BV) · 36 pages, 9 Figures
arxiv created 2019/03/04 · openalex publication_date 2019/03/06 · arxiv updated 2020/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a general framework for computer-assisted verification of the presence of symmetry breaking, period-tupling and touch-and-go bifurcations of symmetric periodic orbits for reversible maps. The framework is then adopted to Poincaré maps in reversible autonomous Hamiltonian systems. In order to justify the applicability of the method, we study bifurcations of halo orbits in the Circular Restricted Three Body Problem. We give a computer-assisted proof of the existence of wide branches of halo orbits bifurcating from L1,2,3-Lyapunov families and for wide range of mass parameter. For two physically relevant mass parameters we prove, that halo orbits undergo multiple period doubling, quadrupling and third-order touch-and-go bifurcations.