Motivated by recent applications to entropy theory in dynamical systems, we generalise
notions introduced by Matthews and define weakly weighted and componentwise weakly …

Motivated by the recent introduction of the intrinsic semilattice entropy, we study generalized
quasi-metric semilattices and their categories. We investigate the relationship between …

We study the receptive metric entropy for semigroup actions on probability spaces, inspired
by a similar notion of topological entropy introduced by Hofmann and Stoyanov (Adv Math …

Partial metrics, or the equivalent weightable quasi-metrics, have been introduced in
Matthews (Proc. 8th Summer Conf. on General Topology and Applications; Ann. New York …

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 …

In [Sch00] a bijection has been established, for the case of semilattices, between invariant
partial metrics and semivaluations. Semivaluations are a natural generalization of valuations …

In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for
finitely generated semigroups acting on compact metric spaces from a set-valued view and …

We introduce a new class of abstract structures, which we call generalized ultrametric
semilattices, and in which the meet operation of the semilattice coexists with a generalized …

Many branches of theoretical and applied mathematics require a quantifiable notion of
complexity. One such circumstance is a topological dynamical system—which involves a …

We discuss the Kolmogorov's entropy and Sinai's definition of it; and then define a
deformation of the entropy, called {\it scaling entropy}; this is also a metric invariant of the …