AN ALGORITHMIC APPROACH TO ESTIMATING THE MINIMAL NUMBER OF PERIODIC POINTS FOR SMOOTH SELF-MAPS OF SIMPLY-CONNECTED MANIFOLDS

作者：Graff Grzegorz^*; Pilarczyk Pawel

来源：Topological Methods in Nonlinear Analysis, 2015, 45(1): 273-286.

DOI：10.12775/tmna.2015.014

• Periodic points
• Nielsen number
• Lefschetz number
• fixed point index
• smooth maps
• minimal number of periodic points

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 (2013), 63-84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

• 出版日期2015-3