## An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds.(English)Zbl 1364.37054

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

Zbl 1276.55005

CombTop
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