2021/10/01 by Bingbing Liang, Liang, Bingbing, Enhui Shi +5
Mathematics · #Mathematical Dynamics and Fractals #Advanced Topology and Set Theory #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.2110.00341
Let X be a compact metric space and G a finitely generated group. Suppose ϕ:G→ \rm Homeo(X) is a continuous action. We show that if ϕ is both distal and expansive, then X must be finite. A counterexample is constructed to show the necessity of finite generation condition on G. This is also a supplement to a result due to Auslander-Glasner-Weiss which says that every distal action by a finitely generated group on a zero-dimensional compactum is equicontinuous.