Phys. Rev. E 62, 2119–2134 (2000)Theory and applications of the systematic detection of unstable periodic orbits in dynamical systemsReceived 26 January 2000; published in the issue dated August 2000 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. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.62.2119
DOI:
10.1103/PhysRevE.62.2119
PACS:
05.45.-a
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