Leiye Xu

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math.DS2026

Positive Rokhlin Entropy Implies Infinite $L^{1}$ -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 $L^{1}$ -orbit multiplicity, both…

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…

math.DS2024

Minimal frequently stable is almost automorphic

Leiye Xu, Zongrui Hu

We show that a minimal toplogical dynamical system that is frequently stable if and only if it is almost automorphic.

Positive Rokhlin Entropy Implies Infinite L1-Orbit Multiplicity: A Negative Answer to Thouvenot's Question

Discrete spectrum of probability measures for locally compact group actions

Minimal frequently stable is almost automorphic

Positive Rokhlin Entropy Implies Infinite $L^{1}$ -Orbit Multiplicity: A Negative Answer to Thouvenot's Question