Graff, Grzegorz; Pilarczyk, Paweł An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. (English) Zbl 1364.37054 Topol. Methods Nonlinear Anal. 45, No. 1, 273-286 (2015). Summary: 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, No. 1, 63–84 (2013; Zbl 1276.55005)]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/. MSC: 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 55M20 Fixed points and coincidences in algebraic topology Keywords:periodic point; Nielsen number; Lefschetz number; fixed point index; smooth map; minimal number of periodic points Citations:Zbl 1276.55005 Software:CombTop PDFBibTeX XMLCite \textit{G. Graff} and \textit{P. Pilarczyk}, Topol. Methods Nonlinear Anal. 45, No. 1, 273--286 (2015; Zbl 1364.37054) Full Text: DOI