Symbolic dynamics based method for rigorous study of the existence of short cycles for chaotic systems

Zbigniew Galias, Warwick Tucker

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Abstract

It is shown that the problem of existence of periodic orbits can be studied rigorously by means of a symbolic dynamics approach combined with interval methods. Symbolic dynamics is used to find approximate initial positions of periodic points and interval operators are used to prove the existence of periodic orbits in a neighborhood of the computer generated solution. As an example the Lorenz system is studied. All 2536 periodic orbits of the Poincaré map with the period n ≤ 14 are found.

Original languageEnglish
Title of host publication2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009
Pages1907-1910
Number of pages4
DOIs
Publication statusPublished - 26 Oct 2009
Externally publishedYes
Event2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009 - Taipei, Taiwan
Duration: 24 May 200927 May 2009

Publication series

NameProceedings - IEEE International Symposium on Circuits and Systems
ISSN (Print)0271-4310

Conference

Conference2009 IEEE International Symposium on Circuits and Systems, ISCAS 2009
CountryTaiwan
CityTaipei
Period24/05/0927/05/09

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