A Topological Approach to Bend-Twist Maps with Applications. (5th October 2011)

• Record Type: Journal Article
• Authors: Pascoletti, Anna; Zanolin, Fabio
• Other Names: Berezansky Leonid Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2011(2011)
• Publication Date: 2011-10-05
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2011/612041
• Languages: English
• ISSNs: 1687-9643

Abstract

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.