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)
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Fund Project:Supported by Research Foundation of Bozhou for the Introduction of Talents, Natural Science Foundation of Anhui Province (Grant No.KJ2019A1300). |
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Abstract: |
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. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2021.03.007 |
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