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Theory and Applications of the Systematic Detection of Unstable Periodic Orbits in Dynamical Systems

Detlef Pingel·Peter Schmelcher·Fotis Diakonos·Ofer Biham
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Abstract

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

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Detlef Pingel, Peter Schmelcher, Fotis Diakonos, Ofer Biham. 2000-06-07. Theory and Applications of the Systematic Detection of Unstable Periodic Orbits in Dynamical Systems. https://doi.org/10.1103/physreve.62.2119

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