Rigorous study of short periodic orbits for the Lorenz system

Zbigniew Galias; Warwick Tucker

doi:10.1109/ISCAS.2008.4541530

Rigorous study of short periodic orbits for the Lorenz system

Zbigniew Galias, Warwick Tucker

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

12 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 language	English
Title of host publication	2008 IEEE International Symposium on Circuits and Systems, ISCAS 2008
Pages	764-767
Number of pages	4
DOIs	https://doi.org/10.1109/ISCAS.2008.4541530
Publication status	Published - 19 Sep 2008
Externally published	Yes
Event	IEEE International Symposium on Circuits and Systems 2008 - Seattle, United States of America Duration: 18 May 2008 → 21 May 2008 https://ieeexplore.ieee.org/xpl/conhome/4534149/proceeding (Proceedings)

Publication series

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

Conference

Conference	IEEE International Symposium on Circuits and Systems 2008
Abbreviated title	ISCAS 2008
Country/Territory	United States of America
City	Seattle
Period	18/05/08 → 21/05/08
Internet address	https://ieeexplore.ieee.org/xpl/conhome/4534149/proceeding (Proceedings)

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10.1109/ISCAS.2008.4541530

Cite this

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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.",

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Galias, Z & Tucker, W 2008, Rigorous study of short periodic orbits for the Lorenz system. in 2008 IEEE International Symposium on Circuits and Systems, ISCAS 2008. Proceedings - IEEE International Symposium on Circuits and Systems, pp. 764-767, IEEE International Symposium on Circuits and Systems 2008, Seattle, Washington, United States of America, 18/05/08. https://doi.org/10.1109/ISCAS.2008.4541530

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AU - Tucker, Warwick

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N2 - 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.

AB - 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.

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DO - 10.1109/ISCAS.2008.4541530

M3 - Conference Paper

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SN - 9781424416844

T3 - Proceedings - IEEE International Symposium on Circuits and Systems

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BT - 2008 IEEE International Symposium on Circuits and Systems, ISCAS 2008

T2 - IEEE International Symposium on Circuits and Systems 2008

Y2 - 18 May 2008 through 21 May 2008

ER -

Rigorous study of short periodic orbits for the Lorenz system

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