Relations among Hamiltonian, area-preserving, and non-wandering flows on surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916888330633216 |
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| author | Yokoyama, Tomoo |
| author_facet | Yokoyama, Tomoo |
| contents | This paper gives a topological characterization of Hamiltonian flows with finitely many singular points on compact surfaces, using the concept of ``demi-caractéristique'' in the sense of Poincaré. Furthermore, we describe the relationships and distinctions among the Hamiltonian, divergence-free, and non-wandering properties for continuous flows, which gives an affirmative answer to the problem posed by Nikolaev and Zhuzhoma under the assumption of finitely many singular points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_12124 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Relations among Hamiltonian, area-preserving, and non-wandering flows on surfaces Yokoyama, Tomoo Dynamical Systems This paper gives a topological characterization of Hamiltonian flows with finitely many singular points on compact surfaces, using the concept of ``demi-caractéristique'' in the sense of Poincaré. Furthermore, we describe the relationships and distinctions among the Hamiltonian, divergence-free, and non-wandering properties for continuous flows, which gives an affirmative answer to the problem posed by Nikolaev and Zhuzhoma under the assumption of finitely many singular points. |
| title | Relations among Hamiltonian, area-preserving, and non-wandering flows on surfaces |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2110.12124 |