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International Journal of Differential Equations
Volume 2011 (2011), Article ID 612041, 20 pages
http://dx.doi.org/10.1155/2011/612041
Research Article

A Topological Approach to Bend-Twist Maps with Applications

Department of Mathematics and Computer Science, University of Udine, via delle Scienze 206, 33100 Udine, Italy

Received 26 May 2011; Accepted 21 July 2011

Academic Editor: Leonid Berezansky

Copyright © 2011 Anna Pascoletti and Fabio Zanolin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper we reconsider, in a purely topological framework, the concept of bend-twist map previously studied in the analytic setting by Tongren Ding in (2007). We obtain some results about the existence and multiplicity of fixed points which are related to the classical Poincaré-Birkhoff twist theorem for area-preserving maps of the annulus; however, in our approach, like in Ding (2007), we do not require measure-preserving conditions. This makes our theorems in principle applicable to nonconservative planar systems. Some of our results are also stable for small perturbations. Possible applications of the fixed point theorems for topological bend-twist maps are outlined in the last section.