Let f be a smooth self-map of an m-dimensional (m ≥ 4) closed connected and simply-connected manifold such that the sequence 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-1-2,
author = {Grzegorz Graff and Agnieszka Kaczkowska},
title = {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},
journal = {Annales Polonici Mathematici},
volume = {107},
year = {2013},
pages = {29-48},
zbl = {1286.55002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-1-2}
}
Grzegorz Graff; Agnieszka Kaczkowska. 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. Annales Polonici Mathematici, Tome 107 (2013) pp. 29-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap107-1-2/