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 …

In the realm of topological automorphisms of totally disconnected locally compact groups,
the scale function introduced by Willis in [19] is compared with the topological entropy. We …

We introduce the algebraic entropy for endomorphisms of arbitrary abelian groups,
appropriately modifying existing notions of entropy. The basic properties of the algebraic …

We introduce the algebraic entropy for endomorphisms of arbitrary abelian groups,
appropriately modifying existing notions of entropy. The basic properties of the algebraic …

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) …

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 …

Now we give a third definition of topological entropy of an action T which is based on the
approximation of a compact set F~ K (R q) by its finite subsets. This approach is quite useful …

We introduce a new class of locally compact groups, namely the strongly compactly covered
groups, which are the Hausdorff topological groups G such that every element of G is …

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 …

Let G be a topological group, let φ be a continuous endomorphism of G and let H be a
closed φ-invariant subgroup of G. We study whether the topological entropy is an additive …