A Juzvinski\u{\i} Addition Theorem for Finitely Generated Free Groups Actions

TL;DR

This paper extends the classical entropy addition theorem to actions of finitely generated free groups on skew-product systems, using Bowen's f-invariant, and corrects previous errors in the literature.

Contribution

It generalizes the Juzvinski addition theorem to free group actions on skew-products with specific compact groups, employing Bowen's f-invariant.

Findings

Proves the addition theorem for free group actions on skew-products

Corrects an error from previous work [Bo10c]

Provides examples illustrating the theorem

Abstract

The classical Juzvinski\u{i} Addition Theorem states that the entropy of an automorphism of a compact group decomposes along invariant subgroups. Thomas generalized the theorem to a skew-product setting. Using L. Bowen's f-invariant we prove the addition theorem for actions of finitely generated free groups on skew-products with compact totally disconnected groups or compact Lie groups (correcting an error from [Bo10c]) and discuss examples.