The topology and isochronicity on complex Hamiltonian systems with homogeneous nonlinearities
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929468448178176 |
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| author | Dong, Guangfeng Yang, Jiazhong |
| author_facet | Dong, Guangfeng Yang, Jiazhong |
| contents | In this paper, we study the Hamiltonian differential systems with homogeneous nonlinearity parts on $\mathbb{C}^2$. Firstly, we present a series of topological properties of polynomial Hamiltonian functions, with a particular focus on the characteristics of critical points and non-trivial cycles that vanish at infinity. Secondly, we use these topological properties to derive a complete set of necessary and sufficient conditions for isochronous centers in this class of systems of any degree. Our method avoids tedious computation of the coefficients of normalization occurring in the usual tools to deal with the isochronicity problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07334 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The topology and isochronicity on complex Hamiltonian systems with homogeneous nonlinearities Dong, Guangfeng Yang, Jiazhong Dynamical Systems 37F75, 32S65, In this paper, we study the Hamiltonian differential systems with homogeneous nonlinearity parts on $\mathbb{C}^2$. Firstly, we present a series of topological properties of polynomial Hamiltonian functions, with a particular focus on the characteristics of critical points and non-trivial cycles that vanish at infinity. Secondly, we use these topological properties to derive a complete set of necessary and sufficient conditions for isochronous centers in this class of systems of any degree. Our method avoids tedious computation of the coefficients of normalization occurring in the usual tools to deal with the isochronicity problem. |
| title | The topology and isochronicity on complex Hamiltonian systems with homogeneous nonlinearities |
| topic | Dynamical Systems 37F75, 32S65, |
| url | https://arxiv.org/abs/2311.07334 |