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A criterion for the existence of periodic points based on the eigenvalues of maps induced in cohomology

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Abstract

We present a criterion for the existence of periodic points based on the eigenvalues of maps induced in cohomology for spaces with rational cohomology isomorphic to a tensor product of a graded exterior algebra with generators in odd dimensions and a graded algebra with all elements of even degree. We give a number of natural examples of such spaces and provide some non-trivial ones. We also give a counterexample to a claim in [3] given there without proof.

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  1. Instytut Matematyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6, 30-348, Kraków, Poland

    Michalina Horecka & Paweł Raźny

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  1. Michalina Horecka
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  2. Paweł Raźny
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Correspondence to Paweł Raźny.

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Horecka, M., Raźny, P. A criterion for the existence of periodic points based on the eigenvalues of maps induced in cohomology. Qual. Theory Dyn. Syst. 21, 49 (2022). https://doi.org/10.1007/s12346-022-00580-3

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