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A Juzvinskii addition theorem for finitely generated free group actions

Published online by Cambridge University Press:  01 November 2012

LEWIS BOWEN  and
YONATAN GUTMAN
LEWIS BOWEN
Affiliation:
Mathematics Department, Mailstop 3368, Texas A&M University, College Station, TX 77843-3368, USA (email: [email protected])
YONATAN GUTMAN
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland (email: [email protected])
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Abstract

The classical Juzvinskii 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 in L. Bowen [Nonabelian free group actions: Markov processes, the Abramov–Rohlin formula and Yuzvinskii’s formula. Ergod. Th. & Dynam. Sys.30(6) (2010), 1629–1663]) and discuss examples.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 1 , February 2014 , pp. 95 - 109
Copyright
Copyright © 2012 Cambridge University Press 

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