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

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

2000-06-07

arxiv.org/abs/nlin/0006011v1

Physical Review E 62, 2119 (2000)

Nonlinear Sciences

Chaotic Dynamics

14 pages, 9 figures

Scientific paper

10.1103/PhysRevE.62.2119

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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