Prediction of Dynamical Systems from Time-Delayed Measurements with Self-Intersections

Prediction of Dynamical Systems from Time-Delayed Measurements with Self-Intersections

Explore a 44-minute lecture on predicting dynamical systems using time-delayed measurements with self-intersections. Delve into new versions of the Takens time-delay embedding theorem in both deterministic and probabilistic settings. Examine upper bounds on the decay rate of prediction errors, as conjectured by Schroer, Sauer, Ott, and Yorke. Learn about one-dimensional observable measurements along a system's orbit and their implications for dynamical system prediction. Gain insights from Adam Śpiewak of IM PAN as part of the Simons Semester on Dynamics series.