Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Symbolic analysis for some planar piecewise linear maps

Pages: 1533 - 1548, Volume 9, Issue 6, November 2003      doi:10.3934/dcds.2003.9.1533

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Peter Ashwin - School of Mathematical Sciences, University of Exeter, Exeter EX4 4QE, United Kingdom (email)
Xin-Chu Fu - Department of Mathematics, Shanghai University, Shanghai 200436, China (email)

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.

Keywords:  Linear map on 2-torus, piecewise linear, piecewise isometry, discontinuous dynamical system, coding, symbolic dynamics.
Mathematics Subject Classification:  37D50.

Received: September 2002;      Revised: June 2003;      Available Online: September 2003.