# American Institute of Mathematical Sciences

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January  2012, 32(1): 81-100. doi: 10.3934/dcds.2012.32.81

## Lefschetz sequences and detecting periodic points

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

Received  July 2010 Revised  December 2010 Published  September 2011

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.
Citation: Anna Gierzkiewicz, Klaudiusz Wójcik. Lefschetz sequences and detecting periodic points. Discrete & Continuous Dynamical Systems - A, 2012, 32 (1) : 81-100. doi: 10.3934/dcds.2012.32.81
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