Dynamics of a piecewise rotation
type: Item
instance of: scholarly article
title: Dynamics of a piecewise rotation
zbMATH Open document ID: 0965.37037
author: Arek Goetz
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: This paper deals with the dynamics of systems generalizing interval exchanges to a class of Euclidean two-dimensional piecewise isometries. Due to the lack of hyperbolicity this class exhibits many features of attractors. More precisely, the author investigates noninvertible piecewise isometries in the 2D case with particular interest of the maximal invariant sets and \(\omega\)-limit sets. The main result states that for a certain class of noninvertible piecewise isometries, orbits visiting both atoms in finitely often must accumulate on the boundaries of the attractor consisting of two maximal invariant discs \(D_0\) and \(D_1\). The key idea is the proof of a dynamical and geometric observation about the monotonic behaviour of orbits of the first-return map to one of the atoms.
Mathematics Subject Classification ID: 37E30
Mathematics Subject Classification ID: 37B10
zbMATH DE Number: 1492544
zbMATH Keywords: isometry
zbMATH Keywords: noninvertible
zbMATH Keywords: piecewise map
zbMATH Keywords: attractor
zbMATH Keywords: hyperbolicity
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: dcds.1998.4.593
OpenAlex ID: W2049439154
DOI: 10.3934/DCDS.1998.4.593
description: scientific article; zbMATH DE number 1492544