2023/02/22 by Slutsky, Konstantin
#Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2302.11088
Katok's special representation theorem states that any free ergodic measure-preserving ℝd-flow can be realized as a special flow over a ℤd-action. It provides a multidimensional generalization of the "flow under a function" construction. We prove the analog of Katok's theorem in the framework of Borel dynamics and show that, likewise, all free Borel ℝd-flows emerge from ℤd-actions through the special flow construction using bi-Lipschitz cocycles.