Rigorous study of short periodic orbits for the Lorenz system

Zbigniew Galias, Warwick Tucker

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11 Citations (Scopus)

Abstract

The existence of short periodic orbits for the Lorenz system is studied rigorously. We describe a method for finding all short cycles embedded in a chaotic singular attractor (i.e. an attractor containing an equilibrium). The method uses an interval operator for proving the existence of periodic orbits in regions where it can be evaluated, and bounds for the return time in other regions. The six shortest periodic orbits for the Lorenz system are found.

Original languageEnglish
Title of host publication2008 IEEE International Symposium on Circuits and Systems, ISCAS 2008
Pages764-767
Number of pages4
DOIs
Publication statusPublished - 19 Sep 2008
Externally publishedYes
EventIEEE International Symposium on Circuits and Systems 2008 - Seattle, United States of America
Duration: 18 May 200821 May 2008

Publication series

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

Conference

ConferenceIEEE International Symposium on Circuits and Systems 2008
Abbreviated titleISCAS 2008
CountryUnited States of America
CitySeattle
Period18/05/0821/05/08

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