Theory and applications of the systematic detection of unstable periodic orbits in dynamical systems

Detlef Pingel, Peter Schmelcher, Fotis K. Diakonos, Ofer Biham

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

A topological approach and understanding to the detection of unstable periodic orbits based on a recently proposed method [Phys. Rev. Lett. 78, 4733 (1997)] is developed. This approach provides a classification of the set of transformations necessary for finding the orbits. Applications to the Ikeda and Hénon map are performed, allowing a study of the distributions of Lyapunov exponents for high periods. In particular, the properties of the least unstable orbits up to period 36 are investigated and discussed.

Original languageAmerican English
Pages (from-to)2119-2134
Number of pages16
JournalPhysical Review E
Volume62
Issue number2
DOIs
StatePublished - 2000

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