An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
DOI:
https://doi.org/10.12775/TMNA.2015.014Keywords
Periodic points, Nielsen number, Lefschetz number, fixed point index, smooth maps, minimal number of periodic pointsAbstract
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/}.Downloads
Published
2015-03-01
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1.
PILARCZYK, Paweł and GRAFF, Grzegorz. An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds. Topological Methods in Nonlinear Analysis. Online. 1 March 2015. Vol. 45, no. 1, pp. 273 - 286. [Accessed 6 November 2024]. DOI 10.12775/TMNA.2015.014.
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