Generalization of Lyapunov Center Theorem for Hamiltonian systems via normal forms theory
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916295695400960 |
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| author | Gołębiewska, A. Rybicki, S. |
| author_facet | Gołębiewska, A. Rybicki, S. |
| contents | In this article we formulate and prove sufficient conditions for the existence of trajectories of nonstationary periodic solutions of autonomous Hamiltonian systems in a neighbourhood of equilibria. It is worth pointing out that assumptions of some well-known theorems imply that of our main results. We obtain our results with the use of the theory of normal forms for Hamiltonian matrices and global bifurcation theory for autonomous Hamiltonian systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14053 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalization of Lyapunov Center Theorem for Hamiltonian systems via normal forms theory Gołębiewska, A. Rybicki, S. Classical Analysis and ODEs 37J46, 37J20 In this article we formulate and prove sufficient conditions for the existence of trajectories of nonstationary periodic solutions of autonomous Hamiltonian systems in a neighbourhood of equilibria. It is worth pointing out that assumptions of some well-known theorems imply that of our main results. We obtain our results with the use of the theory of normal forms for Hamiltonian matrices and global bifurcation theory for autonomous Hamiltonian systems. |
| title | Generalization of Lyapunov Center Theorem for Hamiltonian systems via normal forms theory |
| topic | Classical Analysis and ODEs 37J46, 37J20 |
| url | https://arxiv.org/abs/2406.14053 |