Periodic orbits and P stable orbit closures of continuous flows on surfaces
type: Item
instance of: scholarly article
title: Periodic orbits and P stable orbit closures of continuous flows on surfaces
zbMATH Open document ID: 0675.58032
published in: Chinese Annals of Mathematics. Series B
publication date: 1988-01-01T00:00:00Z
review text: This paper deals with the problem of the coexistence of non-zero- homotopic periodic orbits and Poisson stable orbits for flows on surfaces. It is known that on the torus they are incompatible. Let f be a continuous flow on the closed surface M of genus g, \(g\geq 2\), \(r_ 0\) the number of distinct Poisson stable orbit closures, r the number of non-zero-homotopic to each other (in the nonorientable case let \(r_ 1\) \((r_ 2)\) denote the number of such orbits, which, in addition, are one (two)-sided). The main result consists in the following two inequalities: \(r_ 0+r\leq 3g-3,\) if M is orientable, and \(4r_ 0+r_ 1+r_ 2\leq 3g-3\) in the nonorientable case. In both cases equalities are achieved. [See also \textit{N. G. Markley}, Proc. Am. Math. Soc. 25, 413-416 (1970; Zbl 0198.569).]
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 4105918
zbMATH Keywords: non-zero-homotopic periodic orbits
zbMATH Keywords: Poisson stable orbits
zbMATH Keywords: flows
author: Maoan Han
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4105918