In this talk, I will introduce a continuous-time version of the Feldman-Katok pseudometric (FK-pseudometric, for short) for flows, inspired by Ratner’s notion of matching orbit segments. I will then show how it can be used to characterize loosely Bernoulli measures with zero entropy for continuous flows, which we call loosely Kronecker following Ratner’s suggestion, extending the discrete-time result of García-Ramos and Kwietniak to the continuous-time setting. More precisely, I will prove that an ergodic invariant measure for a continuous flow is loosely Kronecker if and only if there exists a full-measure set on which the FK-pseudometric vanishes for every pair of points. I will also discuss a purely topological characterization of topological models of loosely Kronecker measure-preserving flows.
Meeting ID: 852 4277 3200 Passcode: 103121