Computation of symbolic dynamics for two dimensional piecewise affine maps

Lorenzo Sella; Pieter Collins

doi:10.3934/dcdsb.2011.15.739

Computation of symbolic dynamics for two dimensional piecewise affine maps

Lorenzo Sella^*, Pieter Collins

^*Corresponding author for this work

BioMathematics and BioInformatics

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	739-767
Number of pages	29
Journal	Discrete and Continuous Dynamical Systems-series B
Volume	15
Issue number	3
DOIs	https://doi.org/10.3934/dcdsb.2011.15.739
Publication status	Published - 2011

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10.3934/dcdsb.2011.15.739

Cite this

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title = "Computation of symbolic dynamics for two dimensional piecewise affine maps",

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.",

author = "Lorenzo Sella and Pieter Collins",

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AB - 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.

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