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

Computation of symbolic dynamics for two-dimensional piecewise-affine maps

Pages: 739 - 767, Volume 15, Issue 3, May 2011      doi:10.3934/dcdsb.2011.15.739

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Lorenzo Sella - Niels Bohrweg 1, Leiden, 2333 CA, Netherlands (email)
Pieter Collins - Bouillonstraat 8-10, 6211 LH Maastricht, Netherlands (email)

Abstract: In this paper we design and implement an algorithm for computing symbolic dynamics for two dimensional piecewise-affine maps. The algorithm is based on detection of periodic orbits using the Conley index and Szymczak decomposition of Conley index pair. The algorithm is also extended to deal with discontinuous maps. We compare the algorithm with the algorithm based on tangle of fixed points. We apply the algorithms to compute the symbolic dynamics and entropy bounds for the Lozi map.

Keywords:  Two-dimensional piecewise-affine map, Conley index, symbolic dynamics, homoclinic tangles, Lozi map.
Mathematics Subject Classification:  Primary: 37E99, 37B30, 37B40, 37B10.

Received: June 2009;      Revised: June 2010;      Available Online: February 2011.