Bulletin of the
Korean Mathematical Society BKMS

In this paper we introduce and study the notions of topological sensitivity and its stronger forms on semiflows and on product semiflows. We give a relationship between multi-topological sensitivity and thick topological sensitivity on semiflows. We prove that for a Urysohn space $X$, a syndetically transitive semiflow $(T,X,\pi)$ having a point of proper compact orbit is syndetic topologically sensitive. Moreover, it is proved that for a $T_3$ space $X$, a transitive, nonminimal semiflow $(T,X,\pi)$ having a dense set of almost periodic points is syndetic topologically sensitive. Also, wherever necessary examples/counterexamples are given.

Keywords: Semiflows, syndetic transitivity, topological sensitivity, syndetic topological sensitivity

MSC numbers: 37B02, 54B10, 54D99, 22F05

Supported by: The second author is supported by CSIR-SRF Sr.~No. 09/045(1799)/2020-EMR-I for carrying out this research work.