article published yes Grzegorz Graff author Pawel Pilarczyk author 3768D56A-F248-11E8-B48F-1D18A9856A87 HeEd department 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/}. Juliusz Schauder Center for Nonlinear Studies2015 eng 10.12775/TMNA.2015.014 451273 - 286 Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” <i>Topological Methods in Nonlinear Analysis</i>, vol. 45, no. 1, Juliusz Schauder Center for Nonlinear Studies, 2015, pp. 273–86, doi:<a href="https://doi.org/10.12775/TMNA.2015.014">10.12775/TMNA.2015.014</a>. G. Graff and P. Pilarczyk, “An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds,” <i>Topological Methods in Nonlinear Analysis</i>, vol. 45, no. 1. Juliusz Schauder Center for Nonlinear Studies, pp. 273–286, 2015. G. Graff, P. Pilarczyk, Topological Methods in Nonlinear Analysis 45 (2015) 273–286. Graff G, Pilarczyk P. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. <i>Topological Methods in Nonlinear Analysis</i>. 2015;45(1):273-286. doi:<a href="https://doi.org/10.12775/TMNA.2015.014">10.12775/TMNA.2015.014</a> Graff, G., &#38; Pilarczyk, P. (2015). An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. <i>Topological Methods in Nonlinear Analysis</i>. Juliusz Schauder Center for Nonlinear Studies. <a href="https://doi.org/10.12775/TMNA.2015.014">https://doi.org/10.12775/TMNA.2015.014</a> Graff, Grzegorz, and Pawel Pilarczyk. “An Algorithmic Approach to Estimating the Minimal Number of Periodic Points for Smooth Self-Maps of Simply-Connected Manifolds.” <i>Topological Methods in Nonlinear Analysis</i>. Juliusz Schauder Center for Nonlinear Studies, 2015. <a href="https://doi.org/10.12775/TMNA.2015.014">https://doi.org/10.12775/TMNA.2015.014</a>. Graff G, Pilarczyk P. 2015. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. 45(1), 273–286. 15632018-12-11T11:52:44Z2021-01-12T06:51:37Z