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キーワード:
Mathematics, Dynamical Systems, Algebraic Topology, Geometric Topology
要旨:
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.
