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

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.

Cited by in corpus (1)

• Topological characterizations of Hamiltonian flows with finitely many singular points on unbounded surfaces