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

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

Abstrakty

EN

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.

Słowa kluczowe

EN

Periodic points; Nielsen number; Fixed point index; Smooth maps

Kategorie tematyczne

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

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 6
• Strony: 2160-2172

Daty

wydano

2012-12-01

online

2012-10-12

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

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Identyfikatory

DOI

10.2478/s11533-012-0122-7