Bounded homeomorphisms of the open annulus

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We prove a generalization of the Poincaré-Birkhoff theorem for the open annulus showing that if a homeomorphism satisfies a certain twist condition and the nonwandering set is connected, then there is a fixed point. Our main focus is the study of bounded homeomorphisms of the open annulus. We prove a fixed point theorem for bounded homeomorphisms and study the special case of those homeomorphisms possessing at most one fixed point. Lastly we use the existence of rational rotation numbers to prove the existence of periodic orbits.
16 pages, 4 figures

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Dynamical Systems, Primary 37E40; Secondary 37E45, 54H25

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http://salesiana.dossiersoluciones.com/handle/123456789/65047

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0209307
 http://arxiv.org/abs/math/0209307

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arXiv