5 papers · 1 filter
A three-dimensional corner configuration involving the Omega function
Zhuowen Guo, Rongzhong Xiao, Shuhao Zhang
Let denote the number of prime factors of , counted with multiplicity. We prove that if has positive upper Banach density, then there are $(x,y,z)\…
Positive Rokhlin Entropy Implies Infinite -Orbit Multiplicity: A Negative Answer to Thouvenot's Question
Zongrui Hu, Leiye Xu, Shuhao Zhang
We prove that every free ergodic measure-preserving action of a countably infinite amenable group with positive Rokhlin entropy has infinite complex -orbit multiplicity, both…
Fractal transference principles for subsets of of positive density
Zhuowen Guo, Kangbo Ouyang, Jiahao Qiu +1
We establish a multidimensional fractal transference principle for digit-restricted sets associated with subsets of , extending the one-dimensional framework of Nakaj…
Independence and mean sensitivity in minimal systems under group actions
Chunlin Liu, Leiye Xu, Shuhao Zhang
In this paper, we mainly study the relation between regularity, independence and mean sensitivity for minimal systems. In the first part, we show that if a minimal system is incont…
Independence, sequence entropy and mean sensitivity for invariant measures
Chunlin Liu, Leiye Xu, Shuhao Zhang
We investigate the connections between independence, sequence entropy, and mean sensitivity for a measure preserving system under the action of a countable infinite discrete group.…