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2011 A Topological Approach to Bend-Twist Maps with Applications
Anna Pascoletti, Fabio Zanolin
Int. J. Differ. Equ. 2011(SI2): 1-20 (2011). DOI: 10.1155/2011/612041


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.


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Anna Pascoletti. Fabio Zanolin. "A Topological Approach to Bend-Twist Maps with Applications." Int. J. Differ. Equ. 2011 (SI2) 1 - 20, 2011.


Received: 26 May 2011; Accepted: 21 July 2011; Published: 2011
First available in Project Euclid: 26 January 2017

zbMATH: 1246.37066
MathSciNet: MR2843505
Digital Object Identifier: 10.1155/2011/612041

Rights: Copyright © 2011 Hindawi


Vol.2011 • No. SI2 • 2011
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