Heteroclinic orbits between static classes of time periodic Tonelli Lagrangian systems

Guowei Yu; Guowei Yu

doi:10.3934/era.2022116

Electronic Research Archive

2022, Volume 30, Issue 6: 2283-2302. doi: 10.3934/era.2022116

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Heteroclinic orbits between static classes of time periodic Tonelli Lagrangian systems

Guowei Yu ^,

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

Received: 23 September 2021 Revised: 19 December 2021 Accepted: 03 January 2022 Published: 21 April 2022

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.
- Lagrangian systems,
- heteroclinic orbits,
- action minimizers,
- Aubry-Mather theory
Citation: Guowei Yu. Heteroclinic orbits between static classes of time periodic Tonelli Lagrangian systems[J]. Electronic Research Archive, 2022, 30(6): 2283-2302. doi: 10.3934/era.2022116

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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.

References

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