A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems. (14th July 2013)

• Record Type: Journal Article
• Authors: Pascoletti, Anna; Zanolin, Fabio
• Other Names: Peris Alfredo Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2013(2013)
• Publication Date: 2013-07-14
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2013/267393
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : 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.