3 papers
math.DS2026
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…
math.NT2026
Bohr obstructions to recurrence along Hardy-field sequences
Kangbo Ouyang, Saúl RodrÃguez-MartÃn, Leiye Xu +1
We construct Bohr obstructions to multiple recurrence along rounded Hardy-field sequences, showing that the real derivative-span criterion of Bergelson, Moreira, and Richter is ess…
math.DS2025
Discrete spectrum of probability measures for locally compact group actions
Zongrui Hu, Xiao Ma, Leiye Xu +1
In this paper, we investigate the discrete spectrum of probability measures for actions of locally compact groups. We establish that a probability measure has a discrete spectrum i…