Strongly Rigid Flows

Abstract

We consider flows $(X,T)$, given by actions $(t,x)\to tx$, on a compact metric space $X$ with a discrete $T$ as an acting group. We study a new class of flows - the \textsc{Strongly Rigid} ($\mathbf{SR}$) \ flows, that are properly contained in the class of distal ($\mathbf{D}$) flows and properly contain the class of all equicontinuous ($\mathbf{EQ}$) flows. Thus, $\mathbf{EQ}\text{flows}⫋\mathbf{SR}\text{flows}⫋\mathbf{D}\text{flows}$. The concepts of equicontinuity, strong rigidity and distality coincide for the induced flow $(2^X,T)$. We observe that strongly rigid $(X,T)$ gives distinct properties for the induced flow $(2^X,T)$ and its enveloping semigroup $E(2^X)$. We further study strong rigidity in case of particular semiflows $(X,S)$, with $S$ being a discrete acting semigroup.

References in corpus (3)

• Dynamics of Induced Systems
• Topological Dynamics of Enveloping Semigroups
• Characterization of Quasifactors