Multiplicity of symmetric brake orbits of asymptotically linear symmetric reversible Hamiltonian systems

Jiachen Mu; Duanzhi Zhang; Jiachen Mu; Duanzhi Zhang

doi:10.3934/era.2022123

Electronic Research Archive

2022, Volume 30, Issue 7: 2417-2427. doi: 10.3934/era.2022123

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Multiplicity of symmetric brake orbits of asymptotically linear symmetric reversible Hamiltonian systems

Jiachen Mu ,
Duanzhi Zhang ^,

School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

Received: 29 September 2021 Revised: 20 December 2021 Accepted: 25 December 2021 Published: 29 April 2022

In this paper, we give the relation between a relative Morse index for two continuous symmetric matrices paths in $ {{\bf R}}^{2n} $ satisfying condition (BS1) and the Maslov-type indices under symmetric brake orbit boundary value of these two symmetric matrices paths. As application, we obtain a multiple existence of symmetric brake orbit solutions of asymptotically linear symmetric reversible Hamiltonian systems.
- symmetric brake orbits,
- reversible,
- Hamiltonian systems,
- Maslov-type index,
- asymptotic linear
Citation: Jiachen Mu, Duanzhi Zhang. Multiplicity of symmetric brake orbits of asymptotically linear symmetric reversible Hamiltonian systems[J]. Electronic Research Archive, 2022, 30(7): 2417-2427. doi: 10.3934/era.2022123

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Abstract

In this paper, we give the relation between a relative Morse index for two continuous symmetric matrices paths in $ {{\bf R}}^{2n} $ satisfying condition (BS1) and the Maslov-type indices under symmetric brake orbit boundary value of these two symmetric matrices paths. As application, we obtain a multiple existence of symmetric brake orbit solutions of asymptotically linear symmetric reversible Hamiltonian systems.

References

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