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A SIMPLE METHOD FOR FINDING TOPOLOGICAL HORSESHOES.

Authors :
QINGDU LI
XIAO-SONG YANG
Source :
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Feb2010, Vol. 20 Issue 2, p467-478. 12p. 1 Color Photograph, 14 Graphs.
Publication Year :
2010

Abstract

This paper presents an efficient method for finding horseshoes in dynamical systems by using several simple results on topological horseshoes. In this method, a series of points from an attractor of a map (or a Poincaré map) are firstly computed. By dealing with the series, we can not only find the approximate location of each short unstable periodic orbit (UPO), but also learn the dynamics of almost every small neighborhood of the attractor under the map or the reverse map, which is very helpful for finding a horseshoe. The method is illustrated with the Hénon map and two other examples. Since it can be implemented with a computer software, it becomes easy to study the existence of chaos and topological entropy by virtue of topological horseshoe. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02181274
Volume :
20
Issue :
2
Database :
Academic Search Index
Journal :
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
Publication Type :
Academic Journal
Accession number :
49505226
Full Text :
https://doi.org/10.1142/S0218127410025545