Abstract
A definition of topological entropy for a free semigroup action is suggested. Suppose that a free semigroup acts on a compact metric space by continuous self-maps. To this action, we assign a skew-product transformation whose fiber entropy is taken to be the entropy of the initial action. The main result is Theorem 1, a topological analogue of the Abramov–Rokhlin formula.
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Bufetov, A. Topological Entropy of Free Semigroup Actions and Skew-Product Transformations. Journal of Dynamical and Control Systems 5, 137–143 (1999). https://doi.org/10.1023/A:1021796818247
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DOI: https://doi.org/10.1023/A:1021796818247