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

Explore a 57-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 in cases where self-intersections occur in the reconstructed attractor. Learn about this research conducted jointly by Adam Śpiewak, Krzysztof Barański, and Yonatan Gutman, as part of the Simons Semester on Dynamics series. Gain insights into the study of one-dimensional observable measurements along a system's orbit and their implications for dynamical system prediction.