Relations among Hamiltonian, area-preserving, and non-wandering flows on surfaces
Dynamical Systems
2025-08-12 v2
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.
Keywords
Cite
@article{arxiv.2110.12124,
title = {Relations among Hamiltonian, area-preserving, and non-wandering flows on surfaces},
author = {Tomoo Yokoyama},
journal= {arXiv preprint arXiv:2110.12124},
year = {2025}
}