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An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds
Abstract
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^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 http://www.pawelpilarczyk.com/combtop/.
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.12775/TMNA.2015.014
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- Copyright (2015 Juliusz Schauder Centre for Nonlinear Studies Nicolaus Copernicus University)
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
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Topological Methods in Nonlinear Analysis
no. 45,
pages 273 - 286,
ISSN: 1230-3429 - Language:
- English
- Publication year:
- 2015
- Bibliographic description:
- Pilarczyk P., Graff G.: An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds// Topological Methods in Nonlinear Analysis. -Vol. 45, nr. 1 (2015), s.273-286
- Verified by:
- Gdańsk University of Technology
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