Tail variational principle and asymptotic h-expansiveness for amenable group actions

Entropy and mixing for amenable group actions

For Γ a countable amenable group consider those actions of Γ as measurepreserving transformations of a standard probability space, written as {Tγ}γ∈Γ acting on (X,F , μ). We say {Tγ}γ∈Γ has completely positive entropy (or simply cpe for short) if for any finite and nontrivial partition P of X the entropy h(T, P ) is not zero. Our goal is to demonstrate what is well known for actions of Z and ev...

The Variational Principle and Complexity of Group Actions

Variational Principle for Relative Tail Pressure

We introduce the relative tail pressure to establish a variational principle for continuous bundle random dynamical systems. We also show that the relative tail pressure is conserved by the principal extension.

The Abramov–rokhlin Entropy Addition Formula for Amenable Group Actions

In this note we show that the entropy of a skew product action of a countable amenable group satisfies the classical formula of Abramov and Rokhlin.

Entropy and the Variational Principle for Actions of Sofic Groups

Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective we develop a more general approach to sofic entropy which produces both measure and topological dynamical invariants, and we establish the variational princi...