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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/267393 |
| Summary: | 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. |
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| ISSN: | 2314-4629 2314-4785 |