Topological Entropy of Free Semigroup Actions and Skew-Product Transformations

Author: Bufetov A.^{1, 2}

Source: Journal of Dynamical and Control Systems, Volume 05, Number 1, January 1999 , pp. 137-143(7)

Publisher: Springer

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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.

Keywords: Topological entropy; free semigroup actions; skew-product transformations

Language: English

Document Type: Research article

Affiliations: 1: Indep 2:

Publication date: 1999-01-01