A bridge theorem for the entropy of semigroup actions

Abstract

The topological entropy of a semigroup action on a totally disconnected locally compact abelian group coincides with the algebraic entropy of the dual action. This relation holds both for the entropy relative to a net and for the receptive entropy of finitely generated monoid actions.

Keywords

• topological entropy
• algebraic entropy
• receptive entropy
• bridge theorem
• semigroup action
• dynamical system
• pontryagin duality
• continuous endomorphism
• locally compact abelian group
• 37b40
• 22b05
• 22d40
• 20k30
• 54h20