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Lefschetz sequences and detecting periodic points

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


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