 

David Richeson and Jim Wiseman
Bounded homeomorphisms of the open annulus


Published: 
April 2, 2003 
Keywords: 
Annulus, PoincaréBirkhoff theorem, twist map, fixed point, nonwandering set, periodic point, rotation number 
Subject: 
Primary 37E40; Secondary 37E45, 54H25 


Abstract
We prove a generalization of the PoincaréBirkhoff
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.


Acknowledgements
The second author was partially supported by the Swarthmore College Research Fund.


Author information
David Richeson:
Dickinson College, Carlisle, PA 17013
richesod@dickinson.edu
http://www.dickinson.edu/~richesod
Jim Wiseman:
Swarthmore College, Swarthmore, PA 19081
jwisema1@swarthmore.edu
http://www.swarthmore.edu/NatSci/jwisema1

