A Topological Approach to Bend-Twist Maps with Applications
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 t...
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| Language: | English |
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Hindawi Limited
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/612041 |
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doaj-45c1b28faa3946ea9814b189a845f3072020-11-24T23:30:32ZengHindawi LimitedInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/612041612041A Topological Approach to Bend-Twist Maps with ApplicationsAnna Pascoletti0Fabio Zanolin1Department of Mathematics and Computer Science, University of Udine, via delle Scienze 206, 33100 Udine, ItalyDepartment of Mathematics and Computer Science, University of Udine, via delle Scienze 206, 33100 Udine, ItalyIn 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.http://dx.doi.org/10.1155/2011/612041 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Anna Pascoletti Fabio Zanolin |
| spellingShingle |
Anna Pascoletti Fabio Zanolin A Topological Approach to Bend-Twist Maps with Applications International Journal of Differential Equations |
| author_facet |
Anna Pascoletti Fabio Zanolin |
| author_sort |
Anna Pascoletti |
| title |
A Topological Approach to Bend-Twist Maps with Applications |
| title_short |
A Topological Approach to Bend-Twist Maps with Applications |
| title_full |
A Topological Approach to Bend-Twist Maps with Applications |
| title_fullStr |
A Topological Approach to Bend-Twist Maps with Applications |
| title_full_unstemmed |
A Topological Approach to Bend-Twist Maps with Applications |
| title_sort |
topological approach to bend-twist maps with applications |
| publisher |
Hindawi Limited |
| series |
International Journal of Differential Equations |
| issn |
1687-9643 1687-9651 |
| publishDate |
2011-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2011/612041 |
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AT annapascoletti atopologicalapproachtobendtwistmapswithapplications AT fabiozanolin atopologicalapproachtobendtwistmapswithapplications AT annapascoletti topologicalapproachtobendtwistmapswithapplications AT fabiozanolin topologicalapproachtobendtwistmapswithapplications |
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1725541284855152640 |