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arXiv · 2110.12124

Relations among Hamiltonian, area-preserving, and non-wandering flows on surfaces

Tomoo Yokoyama
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Abstract

This paper gives a topological characterization of Hamiltonian flows with finitely many singular points on compact surfaces, using the concept of ``demi-caract\'eristique'' in the sense of Poincar\'e. 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.

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Tomoo Yokoyama. 2021-10-23. Relations among Hamiltonian, area-preserving, and non-wandering flows on surfaces. https://arxiv.org/abs/2110.12124

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