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Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

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Central European Journal of Mathematics

Abstract

Let f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of f.

In this paper the invariant J[f] is computed for self-maps of 4-manifold M with dimH 2(M; ℚ) ≤ 4 and estimated for other types of manifolds. We also use J[f] to compare minimization of the number of periodic points in smooth and in continuous categories.

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Authors and Affiliations

  1. Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-233, Gdańsk, Poland

    Grzegorz Graff & Agnieszka Kaczkowska

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  1. Grzegorz Graff
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  2. Agnieszka Kaczkowska
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Correspondence to Grzegorz Graff.

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Graff, G., Kaczkowska, A. Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers. centr.eur.j.math. 10, 2160–2172 (2012). https://doi.org/10.2478/s11533-012-0122-7

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  • DOI: https://doi.org/10.2478/s11533-012-0122-7

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