Infimum of Topological Entropies of Homotopy Classes of Maps on Infra-solvmanifolds of Type (R)
Received:April 29, 2020  Revised:November 13, 2020
Key Words: infimum   topological entropy   homotopy   infra-solvmanifolds of type (R)
Fund Project:Supported by Research Foundation of Bozhou for the Introduction of Talents, Natural Science Foundation of Anhui Province (Grant No.KJ2019A1300).
 Author Name Affiliation Baojun HUANG Department of Electronic and Information Engineering, Bozhou University, Anhui 236800, P. R. China School of Mathematical Science, Huaibei Normal University, Anhui 235000, P. R. China
Hits: 310
Let $f$ be a continuous map on infra-solvmanifold $M$ of type (R) and $N^{\infty}(f)$ be the asymptotic Nielsen number of $f$. In this paper, the sufficient conditions to assure that $\log N^{\infty}(f)$ is the infimum of topological entropies of the homotopy class of the map $f$ are given by using Nielsen fixed point theory. These conclusions will generalize the similar results on infra-nilmanifolds.