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Topological pressure and topological entropy of a semigroup of maps. (English) Zbl 1234.37011

Using the Caratheodory-Pesin structure with respect to an arbitrary subset, the topological pressure and topological entropy, introduced for a single continuous map, is generalized to the cases of a semigroup of continuous maps. Topological pressure and lower and upper capacity topological pressure of a semigroup of maps are defined and studied. The relation between two kinds of topological entropies of a semigroup of maps is studied and some properties are shown.

MSC:

37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37B40 Topological entropy
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