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Research Article | Open Access

Heteroclinic orbits between static classes of time periodic Tonelli Lagrangian systems

Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, China
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Abstract

In this paper, we show the existence of heteroclinic orbits between two different static classes of the Aubry set of a Tonelli Lagrangian when the Aubry set has only finite static classes (which is a generic condition in the sense of Mañé) and the Mañé set satisfies certain isolated condition.

Keywords

Lagrangian systemsheteroclinic orbitsaction minimizersAubry-Mather theory

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Electronic Research Archive
Volume 30 Issue 6,
June 2022
Pages 2283-2302
DOI: 10.3934/era.2022116

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Cite this article:
Yu G. Heteroclinic orbits between static classes of time periodic Tonelli Lagrangian systems. Electronic Research Archive, 2022, 30(6): 2283-2302. https://doi.org/10.3934/era.2022116

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Received: 23 September 2021
Revised: 19 December 2021
Accepted: 03 January 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)