Combinatorial scheme of finding minimal number of periodic points for smooth selfmaps of simply connected manifolds
Abstract
Let M be a closed smooth connected and simply connected manifold of dimension m at least 3, and let r be a fixed natural number. The topological invariant D^m_r [f], defined by the authors in [Forum Math. 21 (2009), 491509], is equal to the minimal number of rperiodic points in the smooth homotopy class of f, a given selfmap of M. In this paper, we present a general combinatorial scheme of computing D^m_r [f] for arbitrary dimension m ≥ 4. Using this approach we calculate the invariant in case r is a product of different odd primes. We also obtain an estimate for D^m_r [f] from below and above for some other natural numbers r.
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 Category:
 Articles
 Type:
 artykuł w czasopiśmie wyróżnionym w JCR
 Published in:

Journal of Fixed Point Theory and Applications
no. 13,
edition 1,
pages 63  84,
ISSN: 16617738  Language:
 English
 Publication year:
 2012
 Bibliographic description:
 Graff G., Jezierski J.: Combinatorial scheme of finding minimal number of periodic points for smooth selfmaps of simply connected manifolds// Journal of Fixed Point Theory and Applications. Vol. 13, iss. 1 (2012), s.6384
 DOI:
 Digital Object Identifier (open in new tab) 10.1007/s1178401200761
 Verified by:
 Gdańsk University of Technology
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