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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.01279 |
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| _version_ | 1866909447128875008 |
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| author | Jin, Liang Yan, Jun Zhao, Kai |
| author_facet | Jin, Liang Yan, Jun Zhao, Kai |
| contents | This paper is a continuation of our study of the dynamics of contact Hamiltonian systems in \cite{JY}, but without monotonicity assumption. Due to the complexity of general cases, we focus on the behavior of action minimizing orbits. We pick out certain action minimizing invariant sets $\{\widetilde{\mathcal{N}}_u\}$ in the phase space naturally stratified by solutions $u$ to the corresponding Hamilton-Jacobi equation. Using an extension of characteristic method, we establish the existence of semi-infinite orbits that is asymptotic to some $\widetilde{\mathcal{N}}_u$ and heteroclinic orbits between $\widetilde{\mathcal{N}}_u$ and $\widetilde{\mathcal{N}}_v$ for two different solutions $u$ and $v$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01279 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the dynamics of contact Hamiltonian systems II: Variational construction of asymptotic orbits Jin, Liang Yan, Jun Zhao, Kai Dynamical Systems This paper is a continuation of our study of the dynamics of contact Hamiltonian systems in \cite{JY}, but without monotonicity assumption. Due to the complexity of general cases, we focus on the behavior of action minimizing orbits. We pick out certain action minimizing invariant sets $\{\widetilde{\mathcal{N}}_u\}$ in the phase space naturally stratified by solutions $u$ to the corresponding Hamilton-Jacobi equation. Using an extension of characteristic method, we establish the existence of semi-infinite orbits that is asymptotic to some $\widetilde{\mathcal{N}}_u$ and heteroclinic orbits between $\widetilde{\mathcal{N}}_u$ and $\widetilde{\mathcal{N}}_v$ for two different solutions $u$ and $v$. |
| title | On the dynamics of contact Hamiltonian systems II: Variational construction of asymptotic orbits |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2501.01279 |