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  The Nielsen numbers of iterations of maps on infra-solvmanifolds of type (R) and periodic points

Fel'shtyn, A., & Lee, J. B. (2018). The Nielsen numbers of iterations of maps on infra-solvmanifolds of type (R) and periodic points. Journal of Fixed Point Theory and Applications, 20(2): 62. doi:10.1007/s11784-018-0541-6.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0003-FCC4-4 Version Permalink: https://hdl.handle.net/21.11116/0000-0009-E2FB-D
Genre: Journal Article
Latex : The Nielsen numbers of iterations of maps on infra-solvmanifolds of type $R$ and periodic points

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 Creators:
Fel'shtyn, Alexander1, Author           
Lee, Jong Bum, Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Dynamical Systems, Algebraic Topology, Geometric Topology
 Abstract: We study the asymptotic behavior of the sequence of the Nielsen numbers
$\{N(f^k)\}$, the essential periodic orbits of $f$ and the homotopy minimal periods of $f$ using the Nielsen theory of maps $f$ on infra-solvmanifolds of type $R$. We give a linear lower bound for the number of essential periodic orbits of such a map, which sharpens well-known results of Shub and Sullivan for periodic points and of Babenko and Bogatyi for periodic orbits. We also verify that a constant multiple of infinitely many prime numbers occur as
homotopy minimal periods of such a map.

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Language(s): eng - English
 Dates: 2018
 Publication Status: Issued
 Pages: 31 pp.
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 Rev. Type: Peer
 Identifiers: arXiv: 1403.7631
URI: http://arxiv.org/abs/1403.7631
DOI: 10.1007/s11784-018-0541-6
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Title: Journal of Fixed Point Theory and Applications
  Abbreviation : J. Fixed Point Theory Appl.
Source Genre: Journal
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Pages: - Volume / Issue: 20 (2) Sequence Number: 62 Start / End Page: - Identifier: -