Specification and thermodynamical properties of semigroup actions (Q2814221)

In this paper, the authors study dynamical systems of finitely-generated semigroup actions using the thermodynamic formalism. They introduce new definitions of \textit{topological pressure} and \textit{topological entropy} using a generalisation of the specification property. (One important aspect of these definitions is that they explicitly depend on the generators, but are independent of the growth rate of the semigroup.) They then apply this theory to expanding maps and deduce function-theoretic aspects of the topological pressure. Finally, they end with interesting examples.