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arXiv · 1403.7631

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

Alexander Fel'shtyn·Jong Bum Lee
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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 $f$ by 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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Alexander Fel'shtyn, Jong Bum Lee. 2014-03-29. The Nielsen numbers of iterations of maps on infra-solvmanifolds of type $R$ and periodic points. https://arxiv.org/abs/1403.7631

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