COMPUTATION OF SYMBOLIC DYNAMICS FOR TWO-DIMENSIONAL PIECEWISE-AFFINE MAPS

被引：0
|
作者：
Sella, Lorenzo
Collins, Pieter
机构：
[1] Niels Bohrweg 1, Leiden
[2] Bouillonstraat
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2011年 / 15卷 / 03期
关键词：
Two-dimensional piecewise-affine map; Conley index; symbolic dynamics; homoclinic tangles; Lozi map;
D O I：
10.3934/dcdsb.2011.15.739
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：739 / 767
页数：29
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