(R)型准可解流形上映射同伦类的拓扑熵的下确界

Infimum of Topological Entropies of Homotopy Classes of Maps on Infra-solvmanifolds of Type (R)

中文关键词:  下确界  拓扑熵  同论  (R)型准可解流形

英文关键词:infimum  topological entropy  homotopy  infra-solvmanifolds of type (R)

中文摘要:

      设$f$是(R)型准可解流形$M$上的连续自映射, $N^\infty(f)$是$f$的渐近Nielsen数,本文将利用Nielsen不动点理论,给出$\log\,N^\infty(f)$是$f$的映射同伦类的拓扑熵的下确界的充分条件,这些条件将推广准幂零流形上的类似结果.

英文摘要:

      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.