Syndetic sensitivity in semiflows
It is well known that the Devaney's definition of chaos from 1989 initially had one redundant condition; this fact was proven by \textit{J. Banks} et al. [Am. Math. Mon. 99, No. 4, 332--334 (1992; Zbl 0758.58019)]. Since that time, many authors have published results in this spirit, showing that transitivity and density of periodic points (or variants thereof) imply sensitive dependence on initial conditions (in one sense or another). This article analyses this problem in the context of semiflows given by actions of abelian unital topological semigroups. It generalizes two previous results by other authors. The main result of the paper is the following: If a syndetically transitive semiflow is not minimal, then it is syndetically sensitive.
scientific article; zbMATH DE number 6509429
scientific article