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

2021/10/23 by Tomoo Yokoyama, Yokoyama, Tomoo
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2110.12124

openalex publication_date 2021/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Decompositions of surface flows

Related

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