Symbolic analysis for some planar piecewise linear maps

Copyright © 2003 American Institute of Mathematical Sciences. This is the pre-print version of the article published in Discrete and Continuous Dynamical Systems - Series A (DCDS-A) Vol. 9, pp. 1533-1548, DOI: 10.3934/dcds.2003.9.1533In 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