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

Detlef Pingel, Peter Schmelcher, Fotis K. Diakonos, and Ofer Biham
Phys. Rev. E 62, 2119 – Published 1 August 2000
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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.

  • Received 26 January 2000

DOI:https://doi.org/10.1103/PhysRevE.62.2119

©2000 American Physical Society

Authors & Affiliations

Detlef Pingel and Peter Schmelcher

  • Theoretical Chemistry, Institute for Physical Chemistry, INF 229, University of Heidelberg, 69120 Heidelberg, Germany

Fotis K. Diakonos

  • Department of Physics, University of Athens, GR-15771 Athens, Greece

Ofer Biham

  • Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel

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Vol. 62, Iss. 2 — August 2000

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