Probabilistic Takens delay embedding theorem

This lecture covers the Probabilistic Takens delay embedding theorem, which discusses the reconstruction of phase spaces using time-delayed measurements of observables. It explores various versions of the theorem for different types of dynamical systems and perturbations, emphasizing the conditions for successful embedding. The lecture also delves into the application of the theorem in reconstructing attractors, linear embeddings, and injective projections. Additionally, it presents examples and properties related to the inverse map, providing insights into the probabilistic aspects of the embedding process.