In this expository paper we describe an unifying approach for many known entropies in
Mathematics. First we recall the notion of semigroup entropy h_S in the category S of …

We present a unifying approach to the study of entropies in Mathematics, such as measure
entropy, topological entropy, algebraic entropy, set-theoretic entropy. We take into account …

Let G be a set and let s be a net of finite subsets of G. If pS, vq is a pre-normed semigroup,
that is, a semigroup S together with a non-negative real-valued function v, we introduce a …

We provide a unifying approach which links results on algebraic actions by Lind and
Schmidt, Chung and Li, and a topological result by Meyerovitch that relates entropy to the …

The notion of entropy appears in many fields and this paper is a survey about entropies in
several branches of Mathematics. We are mainly concerned with the topological and the …

This paper deals with the problem of finding the range of entropy values resulting from
actions of discrete amenable groups by automorphisms of compact abelian groups. When …

This is the first part in a series in which sofic entropy theory is generalized to class-bijective
extensions of sofic groupoids. Here we define topological and measure entropy and prove …

arXiv:2401.10012v1 [math.DS] 18 Jan 2024 Page 1 arXiv:2401.10012v1 [math.DS] 18 Jan
2024 Local entropy theory and applications Felipe Garcıa-Ramos and Hanfeng Li Abstract …

In recent years there has been a great deal of progress in the study of actions of countable
groups. In particular, the concept of the entropy of an action has been extended to all sofic …

Let G be a discrete group which admits an amenable action on a compact space
and\gamma\in\textrm {Aut}(G) be an automorphism. We define a notion of entropy …