Computation of symbolic dynamics for one-dimensional maps

被引：5

作者：

Sella, Lorenzo ^{[1
]}

Collins, Pieter ^{[1
]}

机构：

[1] Ctr Wiskunde & Informat, NL-1090 GB Amsterdam, Netherlands

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 234卷 / 02期

关键词：

One-dimensional map; Kneading theory; Symbolic dynamics; Interval arithmetic; TOPOLOGICAL-ENTROPY; KNEADING THEORY; INVARIANTS; INTERVAL;

D O I：

10.1016/j.cam.2009.12.034

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 rigorous algorithms for computing symbolic dynamics for piecewise-monotone-continuous maps of the interval. The algorithms are based on computing forwards and backwards approximations of the boundary, discontinuity and critical points. We explain how to handle the discontinuities in the symbolic dynamics which occur when the computed partition element boundaries are not disjoint. The method is applied to compute the symbolic dynamics and entropy bounds for the return map of the singular limit of a switching system with hysteresis and the forced Van der Pol equation. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：418 / 436

页数：19

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