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

Anna Pascoletti | Zendy; Fabio Zanolin | Zendy

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

Author(s) -

Anna Pascoletti,

Fabio Zanolin

Publication year - 2013

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2013/267393

Subject(s) - mathematics , invariant (physics) , lemma (botany) , planar , topology (electrical circuits) , pure mathematics , dynamical systems theory , topological conjugacy , topological dynamics , rotation number , combinatorics , mathematical physics , physics , computer science , ecology , computer graphics (images) , poaceae , quantum mechanics , biology , biochemistry , chemistry , topological tensor product , functional analysis , gene

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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