Entropy theory for sofic groupoids I: the foundations
Dynamical Systems
2013-03-19 v2
Abstract
This is the first part in a series in which sofic entropy theory is generalized to class-bijective extensions of sofic groupoids. Here we define topological and measure entropy and prove invariance. We also establish the variational principle, compute the entropy of Bernoulli shift actions and answer a question of Benjy Weiss pertaining to the isomorphism problem for non-free Bernoulli shifts. The proofs are independent of previous literature.
Cite
@article{arxiv.1210.1992,
title = {Entropy theory for sofic groupoids I: the foundations},
author = {Lewis Bowen},
journal= {arXiv preprint arXiv:1210.1992},
year = {2013}
}
Comments
(86 pages) Comments welcome! This new version corrects a number of minor errors in the previous one