TY - JOUR
AU - Pilarczyk, PaweÅ‚
AU - Graff, Grzegorz
PY - 2015/03/01
Y2 - 2022/10/04
TI - An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 45
IS - 1
SE -
DO - 10.12775/TMNA.2015.014
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2015.014
SP - 273 - 286
AB - For a given self-map $f$ of $M$, a closed smooth connected and simply-connected manifold of dimension $m\geq 4$, we provide an algorithm for estimating the values of the topological invariant $D^m_r[f]$, which equals the minimal number of $r$-periodic points in the smooth homotopy class of $f$. Our results are based on the combinatorial scheme for computing $D^m_r[f]$ introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63-84]. An open-source implementation of the algorithm programmed in C++ is publicly available at {\tt http://www.pawelpilarczyk.com/combtop/}.
ER -