Infinitely many Brake orbits of Tonelli Hamiltonian systems on the cotangent bundle
Dynamical Systems
2023-02-21 v1 Classical Analysis and ODEs
Functional Analysis
Symplectic Geometry
Abstract
We prove that on the twisted cotangent bundle of a closed manifold with an exact magnetic form, a Hamiltonian system of a time-dependent Tonelli Hamiltonian function possesses infinitely many brake orbits. More precisely, by applying Legendre transform we show that there are infinitely many symmetric orbits of the dual Euler-Lagrange system on the configuration space. This result contains an assertion for the existence of infinitely many symmetric orbits of Tonelli Euler-Lagrange systems given by G. Lu at the end of [Lu09a, Remark 6.1]. In this paper, we will present a complete proof of this assertion.
Keywords
Cite
@article{arxiv.2302.09472,
title = {Infinitely many Brake orbits of Tonelli Hamiltonian systems on the cotangent bundle},
author = {Duanzhi Zhang and Zhihao Zhao},
journal= {arXiv preprint arXiv:2302.09472},
year = {2023}
}