title: Theory and applications of the systematic detection of unstable periodic orbits in dynamical systems
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.
authors.affiliation: Theoretical Chemistry, Institute for Physical Chemistry, INF 229, University of Heidelberg, 69120 Heidelberg, Germany.
authors.initials: D
authors.lastname: Pingel
authors.initials: P
authors.lastname: Schmelcher
authors.initials: FK
authors.lastname: Diakonos
authors.initials: O
authors.lastname: Biham