Bounded homeomorphisms of the open annulus

Details Bounded homeomorphisms of the open annulus Bounded homeomorphisms of the open annulus

2002-09-23

arxiv.org/abs/math/0209307v1

Mathematics

Dynamical Systems

16 pages, 4 figures

Scientific paper

We prove a generalization of the Poincar\'e-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.

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