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Specification and thermodynamical properties of semigroup actions. (English) Zbl 1353.37065

In this paper, the authors study dynamical systems of finitely-generated semigroup actions using the thermodynamic formalism. They introduce new definitions of topological pressure and 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.

MSC:

37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems
37B40 Topological entropy
37F15 Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems

Citations:

Zbl 0278.28012
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References:

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