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Theory and applications of the systematic detection of unstable periodic orbits in dynamical systems
1Theoretical Chemistry, Institute for Physical Chemistry, INF 229, University of Heidelberg, 69120 Heidelberg, Germany.
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 Henon 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.
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