Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers

• Autorzy: Grzegorz Graff , Agnieszka Kaczkowska
• Języki publikacji: EN

Abstrakty

EN

Let f be a smooth self-map of an m-dimensional (m ≥ 4) closed connected and simply-connected manifold such that the sequence ${L(fⁿ)}_{n=1}^{∞}$ of the Lefschetz numbers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defined in combinatorial terms and is constant for all sufficiently large r. We compute J[f] for self-maps of some manifolds with simple structure of homology groups.

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 37C05: Smooth mappings and diffeomorphisms
• 37C25: Fixed points, periodic points, fixed-point index theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2013
• Tom: 107
• Numer: 1
• Strony: 29-48

Daty

wydano

2013

Twórcy

autor

Grzegorz Graff

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

autor

Agnieszka Kaczkowska

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

Identyfikatory

DOI

10.4064/ap107-1-2