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Combinatorial scheme of finding minimal number of periodic points for smooth self-maps 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), 491-509], is equal to the minimal number of r-periodic points in the smooth homotopy class of f, a given self-map 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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- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s11784-012-0076-1
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
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Journal of Fixed Point Theory and Applications
no. 13,
edition 1,
pages 63 - 84,
ISSN: 1661-7738 - Language:
- English
- Publication year:
- 2012
- Bibliographic description:
- Graff G., Jezierski J.: Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds// Journal of Fixed Point Theory and Applications. -Vol. 13, iss. 1 (2012), s.63-84
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s11784-012-0076-1
- Verified by:
- Gdańsk University of Technology
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