Symbolic analysis for some planar piecewise linear maps

Peter Ashwin; Xin-Chu Fu

doi:10.3934/dcds.2003.9.1533

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2003, Volume 9, Issue 6: 1533-1548. Doi: 10.3934/dcds.2003.9.1533

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Symbolic analysis for some planar piecewise linear maps

Peter Ashwin^1, and
Xin-Chu Fu^2,

1.
School of Mathematical Sciences, University of Exeter, Exeter EX4 4QE
2.
Department of Mathematics, Shanghai University, Shanghai 200436

Received: August 31, 2002

Revised: May 31, 2003

Published: October 2003

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Abstract

In this paper a class of linear maps on the 2-torus and some planar piecewise isometries are discussed. For these discontinuous maps, by introducing codings underlying the map operations, symbolic descriptions of the dynamics and admissibility conditions for itineraries are given, and explicit expressions in terms of the codings for periodic points are presented.

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Mathematics Subject Classification: 37D50.

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