Seminar Talk

Many real-world systems exhibit dynamical chaos, characterized by sensitive dependence on initial conditions and intricate, seemingly disordered behavior. While existing abstract tools from smooth ergodic theory provide a rich framework for understanding chaotic dynamics, verifying this framework in concrete systems remains a notoriously difficult problem. Even in low-dimensional toy models, rigorous proofs often lag significantly behind compelling numerical evidence. Remarkably, this problem becomes far more tractable when systems are subjected to external, time-dependent stochastic forcing. In such settings, the scope of systems for which chaotic hallmarks can be rigorously established expands dramatically, offering substantive progress toward the original promise of chaos theory: to explain and quantify dynamical disorder in nature. I will present several applications of these ideas, including towards disordered dynamical behavior exhibited in systems from fluid mechanics. This talk will include joint work with many collaborators, including Lai-Sang Young, Jinxin Xue, Jacob Bedrossian, and Sam Punshon-Smith.