Lefschetz sequences and detecting periodic points

Anna Gierzkiewicz; Klaudiusz Wójcik

doi:10.3934/dcds.2012.32.81

Article Contents

2012, Volume 32, Issue 1: 81-100. Doi: 10.3934/dcds.2012.32.81

This issue Previous Article Global regularity and asymptotic behavior of modified Navier-Stokes equations with fractional dissipation Next Article Traveling wave solution for a lattice dynamical system with convolution type nonlinearity

Lefschetz sequences and detecting periodic points

Anna Gierzkiewicz^1, and
Klaudiusz Wójcik^2,

1.
Department of Applied Mathematics, University of Agriculture in Krakow, Balicka 253c, 30-198 Kraków
2.
Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków

Received: June 30, 2010

Revised: November 30, 2010

Published: December 2011

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Abstract

We introduce a dual sequence condition (DSC) for a discrete dynamical system given by a continuous map $f:X\to X$ of some metric space $X$. It is defined in terms of the Lefschetz sequence and its dual sequence of the endomorphism of a graded vector space of finite type associated to the dynamical system $f$. We prove the arithmetical properties of the dual Lefschetz sequence and we show some of its dynamical consequences, mainly concerning the topological methods for detecting chaotic dynamics.

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Mathematics Subject Classification: Primary: 37B30, 37B10; Secondary: 37B40.

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