Periodic Solutions, KAM Tori, and Bifurcations in the Planar Anisotropic Schwarzschild-Type Problem

DOI10.1137/21m1450409zbMath1528.37050MaRDI QIDQ6174011

Angelo Alberti, Jhon Vidarte, Claudio Vidal

Publication date: 13 July 2023

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

periodic solutionslinear stabilitybifurcationsKAM toriaveragingsymmetric periodic solutionsReeb's theoremnormalization and reductionreduced space and invariantsSchwarzschild potential

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Nearly integrable Hamiltonian systems, KAM theory (70H08) Averaging of perturbations for nonlinear problems in mechanics (70K65) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

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