A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems
We present a topological result, named crossing lemma, dealing with the existence of a continuum which crosses a topological space between a pair of “opposite” sides. This topological lemma allows us to obtain some fixed point results. In the works of Pascoletti et al., 2008, and Pascoletti and Zano...
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/267393 |
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| author | Anna Pascoletti Fabio Zanolin |
| author_facet | Anna Pascoletti Fabio Zanolin |
| author_sort | Anna Pascoletti |
| collection | DOAJ |
| description | We present a topological result, named crossing lemma, dealing with the existence of a continuum which crosses a topological space between a pair of “opposite” sides. This topological
lemma allows us to obtain some fixed point results. In the works of Pascoletti et al., 2008, and Pascoletti and Zanolin, 2010, we have widely exposed the crossing lemma for planar regions homeomorphic to
a square, and we have also presented some possible applications to the theory of topological horseshoes and to the study of chaotic-like dynamics for planar maps. In this work, we move from the framework of the
generalized rectangles to two other settings (annular regions and invariant sets), trying to obtain similar results. An application to a model of
fluid mixing is given. |
| format | Article |
| id | doaj-art-1a7092b014a2474ba830bf422d7e3ced |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-1a7092b014a2474ba830bf422d7e3ced2025-02-03T01:02:11ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/267393267393A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical SystemsAnna Pascoletti0Fabio Zanolin1Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine, ItalyDipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine, ItalyWe present a topological result, named crossing lemma, dealing with the existence of a continuum which crosses a topological space between a pair of “opposite” sides. This topological lemma allows us to obtain some fixed point results. In the works of Pascoletti et al., 2008, and Pascoletti and Zanolin, 2010, we have widely exposed the crossing lemma for planar regions homeomorphic to a square, and we have also presented some possible applications to the theory of topological horseshoes and to the study of chaotic-like dynamics for planar maps. In this work, we move from the framework of the generalized rectangles to two other settings (annular regions and invariant sets), trying to obtain similar results. An application to a model of fluid mixing is given.http://dx.doi.org/10.1155/2013/267393 |
| spellingShingle | Anna Pascoletti Fabio Zanolin A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems Journal of Mathematics |
| title | A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems |
| title_full | A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems |
| title_fullStr | A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems |
| title_full_unstemmed | A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems |
| title_short | A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems |
| title_sort | crossing lemma for annular regions and invariant sets with an application to planar dynamical systems |
| url | http://dx.doi.org/10.1155/2013/267393 |
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