Minimal number of periodic points for smooth self-maps of simply-connected manifolds

Description

The problem of finding the minimal number of periodic points in a given class of self-maps of a space is one of the central questions in periodic point theory. We consider a closed smooth connected and simply-connected manifold of dimension at least 4 and its self-map f. The topological invariant D_r[f] is equal to the minimal number of r-periodic points in the smooth homotopy class of f. In our analysis we assume that r is odd and all coefficients b(k) of so-called periodic expansion of Lefschetz numbers of iterations are non-zero for all k dividing r and different from 1. We provide the values of the simplified version of the invariant: D_r[f](mod 1) (which is equal either D_r[f] or D_r[f]+1) for all odd r between 1 and 2000 and for manifolds of dimension 4,5,6,7,8,9,10,11,12,13. Our results are based on the combinatorial scheme for computing D_r[f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63-84, https://doi.org/10.1007/s11784-012-0076-1]. The data consists of 5 files dim4_5.txt, dim6_7.txt, dim8_9.txt, dim10_11.txt, dim12_13.txt each of which contains 1000 pairs, where the first place stands for r and the second is the value of the invariant D_r[f](mod 1).

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Dr[f]_dim4-13.zip

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Year of publication:

2020

Verification date:

2020-12-17

Creation date:

2020

Dataset language:

English

Fields of science:

mathematics (Natural sciences)

DOI:

10.34808/c655-7984

Funding:

Topological invariants: the structure of a space and its self-maps

Verified by:

Gdańsk University of Technology

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