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 Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are ba...
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| Format: | article |
| Language: | eng |
| Published: |
2015
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| Online Access: | http://hdl.handle.net/1822/39774 |
| Country: | Portugal |
| Oai: | oai:repositorium.sdum.uminho.pt:1822/39774 |
| Summary: | 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 Dm 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 Dm 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 http://www.pawelpilarczyk.com/combtop/. |
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