An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m≥4, we provide an algorithm for estimating the values of the topological invariant D r m [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 r m [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/.

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