An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

Paweł Pilarczyk, Grzegorz Graff

DOI: http://dx.doi.org/10.12775/TMNA.2015.014

Abstract


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/}.

Keywords


Periodic points; Nielsen number; Lefschetz number; fixed point index,smooth maps; minimal number of periodic points

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