The Li–Yorke definition of chaos proved its value for interval maps. In this paper it is considered in the setting of general topological dynamics. We adopt two opposite points of view. On the one… (More)

For an arbitrary topological group G any compact G-dynamical system (G, X) can be linearly G-represented as a weak∗-compact subset of a dual Banach space V ∗. As was shown in [45] the Banach space V… (More)

Each topological group G admits a unique universal minimal dynamical system (M(G), G). For a locally compact non-compact group this is a nonmetrizable system with a very rich structure, on which G… (More)

A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of βN, or it is a “tame”… (More)

Each topological group G admits a unique universal minimal dynamical system (M(G), G). For a locally compact non-compact group this is a nonmetrizable system with a rich structure, on which G acts… (More)

We show the existence of an infinite monothetic Polish topological group G with the fixed point on compacta property. Such a group provides a positive answer to a question of Mitchell who asked… (More)

For any countable group satisfying the \weak Rohlin property", and for each dynamical property, the set of-actions with that property is either residual or meager. The class of groups with the weak… (More)

Classical ergodic theory deals with measure (or measure class) preserving actions of locally compact groups on Lebesgue spaces. An important tool in this setting is a theorem of Mackey which provides… (More)

For a topological group G we introduce the algebra SUC(G) of strongly uniformly continuous functions. We show that SUC(G) contains the algebra WAP (G) of weakly almost periodic functions as well as… (More)

This paper treats the Pinsker algebra of a dynamical system in a way which avoids the use of an ordering on the acting group. This enables us to prove some of the classical results about entropy and… (More)