A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems

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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Main Authors: Anna Pascoletti, Fabio Zanolin
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2013/267393
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spelling doaj-1a7092b014a2474ba830bf422d7e3ced2020-11-24T23:23:09ZengHindawi LimitedJournal 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
collection DOAJ
language English
format Article
sources DOAJ
author Anna Pascoletti
Fabio Zanolin
spellingShingle Anna Pascoletti
Fabio Zanolin
A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems
Journal of Mathematics
author_facet Anna Pascoletti
Fabio Zanolin
author_sort Anna Pascoletti
title 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_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_sort crossing lemma for annular regions and invariant sets with an application to planar dynamical systems
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2013-01-01
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.
url http://dx.doi.org/10.1155/2013/267393
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AT fabiozanolin acrossinglemmaforannularregionsandinvariantsetswithanapplicationtoplanardynamicalsystems
AT annapascoletti crossinglemmaforannularregionsandinvariantsetswithanapplicationtoplanardynamicalsystems
AT fabiozanolin crossinglemmaforannularregionsandinvariantsetswithanapplicationtoplanardynamicalsystems
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