Lebesgue Orbit Equivalence of Multidimensional Borel Flows

2015/04/03 by Konstantin Slutsky, Slutsky, Konstantin
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Logic (math.LO) #Mathematical Dynamics and Fractals #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1504.00958

openalex publication_date 2015/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main result of the paper is classification of free multidimensional Borel flows up to Lebesgue Orbit Equivalence, by which we understand an orbit equivalence that preserves the Lebesgue measure on each orbit. Two non smooth Euclidean flows are shown to be Lebesgue Orbit Equivalence if and only if they admit the same number of invariant ergodic probability measures.

Related

• Smooth orbit equivalence of multidimensional Borel flows
• Regular cross sections of Borel flows
• Katok's special representation theorem for multidimensional Borel flows
• On time change equivalence of Borel flows
• The analogue of Belinskaya's theorem for measure-preserving flows