Document Type

Article

Publication Date

4-2003

Department

Mathematics

Language

English

Publication Title

New York Journal of Mathematics

Abstract

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.

Comments

This published version is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit New York Journal of Mathematic's Website.

© 2003. The Authors

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