Entropies of a semigroup of maps
The notion of topological entropy introduced originally for homeomorphisms admits several entropy-like invariants in the case of endomorphisms related to the noninvertibility of the map under study. The most known among them are the standard topological entropy, the preimage relation entropy, the preimage branch entropy, and the point entropy. In the present paper, these four entropy-like invariants are generalized to the case of a finitely generated semigroup of continuous transformations of a compact metric space. Relations between those entropies and suitable examples are considered as well.
scientific article; zbMATH DE number 2110779