Homotopic indivisibility of closed orbits of 3-dimensional Anosov flows
type: Item
instance of: scholarly article
title: Homotopic indivisibility of closed orbits of 3-dimensional Anosov flows
zbMATH Open document ID: 0936.37007
DOI: 10.1007/PL00004313
author: Sergio R. Fenley
published in: Mathematische Zeitschrift
publication date: 2000-05-22T00:00:00Z
review text: The author considers 3-dimensional Anosov flows. Closed orbits of such flows have excellent homotopic properties: they always represent non trivial, infinite order elements of the fundamental group. In the paper the author investigates homotopic divisibility of closed orbits of the flow. It is proved that given an Anosov flow \(\Phi\) in \(M^{3}\) so that its stable and unstable foliations are transversely orientable then any closed orbit \(\gamma\) of \(\Phi\) (traversed once) represents an indivisible element in the fundamental group of \(M\). In the non-orientable case the author proves that if a closed orbit \(\gamma\) is freely homotopic to \(\alpha^{n}\), where \(\alpha\) is a closed curve in \(M\), then \(|n |\leq 2\).
Mathematics Subject Classification ID: 37D20
Mathematics Subject Classification ID: 37D40
zbMATH DE Number: 1033935
zbMATH Keywords: Anosov flow
zbMATH Keywords: closed orbit
zbMATH Keywords: fundamental group
zbMATH Keywords: stable
zbMATH Keywords: unstable foliations
MaRDI profile type: Publication
full work available at URL: pl00004313
OpenAlex ID: W2003810873
description: scientific article; zbMATH DE number 1033935