We show that the topological entropy of a continuous endomorphism of a compact abelian
group coincides with the algebraic entropy of the dual endomorphism of the (discrete) …

By analogy with the topological entropy for continuous endomorphisms of totally
disconnected locally compact groups, we introduce a notion of topological entropy for …

For a totally disconnected locally compact abelian group, we prove that the topological
entropy of a continuous endomorphism coincides with the algebraic entropy of the dual …

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 …

Introduction. In their basic paper [1] on topological entropy, a conjugacyinvariant of
continuous mappings, Adler, Konheim, and McAndrew conjectured that, for any …

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 …

The new notion of adjoint algebraic entropy of endomorphisms of Abelian groups is
introduced. Various examples and basic properties are provided. It is proved that the adjoint …

The theory of endomorphism rings of algebraic structures allows, in a natural way, a
systematic approach based on the notion of entropy borrowed from dynamical systems. In …

The theory of endomorphism rings of algebraic structures allows, in a natural way, a
systematic approach based on the notion of entropy borrowed from dynamical systems …

In this paper we will consider entropy of automorphisms on locally compact abelian groups.
Bowen's definition of entropy of a uniformly continuous mapping applies in particular to …