Unpredictable points and stronger versions of Ruelle–Takens and Auslander–Yorke chaos

Abstract

In this paper we generalize the notion of an unpredictable point in a semiflow, introduced by Akhmet and Fen in 2016, to the case of semiflows with arbitrary acting topological monoids. We then introduce the notions of strong Ruelle–Takens and strong Auslander–Yorke chaoticity in semiflows. We use unpredictable points in some statements involving these notions.