Almost sure rotation number of piecewise affine endomorphisms of the circle
type: Item
instance of: scholarly article
title: Almost sure rotation number of piecewise affine endomorphisms of the circle
zbMATH Open document ID: 1035.37029
author: Sylvain Crovisier
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2002-01-01T00:00:00Z
review text: The main result of the paper is the following theorem. Theorem C: A generic \(C^1\) vector field on a closed manifold \(M\) (where the set of \(C^1\) vector field spaces endowed with \(C^1\) topology is considered as a Baire topological space) has either infinitely many homoclinic classes, or else a finite collection of attractors with basins that form an open-dense set, and a finite collection of repellers with basins forming an open-dense set. It gives an approach to a conjecture of Palis. It is proved also that there exists a locally residual subset of \(C^1\) vector fields on a 5-manifold having finitely many attractors and repellers but infinitely many homoclinic classes.
reviewed by: Andrzej Pelczar
Mathematics Subject Classification ID: 37E10
Mathematics Subject Classification ID: 37E45
Mathematics Subject Classification ID: 37C40
zbMATH DE Number: 1890485
zbMATH Keywords: expanding endomorphism of the circle
zbMATH Keywords: almost sure rotation number
zbMATH Keywords: SRB measure
MaRDI profile type: Publication
full work available at URL: s005740200000
OpenAlex ID: W1975607930
DOI: 10.1007/S005740200000
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description: scientific article; zbMATH DE number 1890485