Alex Blumenthal: Tractability of chaotic regimes for dynamical systems with noise

Abstract: Despite the ubiquity of chaotic dynamics in the real world, it remains notoriously difficult to check mathematically whether a given dynamical system has a non-transient chaotic regime. Remarkably, noise has a “regularizing” effect, opening up the study of chaotic dynamics far beyond what is currently possible for purely deterministic systems. This talk will give an overview of some of my results along these lines for two related models: (i) random perturbations of 1d systems (joint w/ Yun Yang), (ii) random perturbations of the Standard map (joint w/ Jinxin Xue and Lai-Sang Young) and (iii) passive scalar advection by an incompressible, time-varying flow (joint w/ Jacob Bedrossian and Sam Punshon-Smith).