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arXiv · 2302.09472

Infinitely many Brake orbits of Tonelli Hamiltonian systems on the cotangent bundle

Duanzhi Zhang·Zhihao Zhao
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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.

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Duanzhi Zhang, Zhihao Zhao. 2023-02-19. Infinitely many Brake orbits of Tonelli Hamiltonian systems on the cotangent bundle. https://arxiv.org/abs/2302.09472

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