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On the index of approximating sets of periodic points

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LetK be a compact space andf:K→K a continuous map without fixed points, i.e. Fixf=⊘. For prime numbersp, the sets Fixf p are freeℤ/p-spaces with theℤ/p-action induced byf. Our aim is to estimate the topological indicesi(F p,f) of invariant subsetsF p⊂Fixf p approximating a givenS⊂K.

We construct an example (K,f,S) withS⊂Fixf q (q being some prime number) such that, for each neighborhoodU ofS, i (Fix (f|u) p, f) increases linearly withp.

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  1. Mathematisches Institut, Universität München, Theresienstr. 39, D-80333, München

    Heinrich Steinlein

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  1. Heinrich Steinlein
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Steinlein, H. On the index of approximating sets of periodic points. Manuscripta Math 89, 15–33 (1996). https://doi.org/10.1007/BF02567502

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  • DOI: https://doi.org/10.1007/BF02567502

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