2016/03/08 by Lewis Bowen, Bowen, Lewis
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1603.02621
openalex publication_date 2016/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dan Rudolph showed that for an amenable group Γ, the generic measure-preserving action of Γ on a Lebesgue space has zero entropy. Here this is extended to nonamenable groups. In fact, the proof shows that every action is a factor of a zero entropy action! This uses the strange phenomena that in the presence of nonamenability, entropy can increase under a factor map. The proof uses Seward's recent generalization of Sinai's Factor Theorem, the Gaboriau-Lyons result and my theorem that for every nonabelian free group, all Bernoulli shifts factor onto each other.