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

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Fel'shtyn,  Alexander
Max Planck Institute for Mathematics, Max Planck Society;

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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.


Cite as: http://hdl.handle.net/21.11116/0000-0003-FCC4-4
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.