Δ-Weakly Mixing Subset In Positive Entropy Actions Of A Nilpotent Group

2019/05/22 by Liu, Kairan
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.08934

Abstract

The notion of Δ-weakly mixing subsets is introduced for countable torsion-free discrete group actions. It is shown that for a finitely generated torsion-free discrete nilpotent group action, positive topological entropy implies the existence of Δ-weakly mixing subsets, and while there exists a finitely generated torsion-free discrete solvable group action which has positive topological entropy but without any Δ-weakly mixing subsets.

Related

• Uniform mixing and completely positive sofic entropy
• Chaotic behavior of group actions
• Local entropy theory for a countable discrete amenable group action
• A van der Corput lemma and weak mixing over groups
• Lowering topological entropy over subsets for amenable group actions