Tangent Space Structure of Cartesian Products of Chaotic Attractors

A comprehensive study is developed for analyzing tangent space structures and geometric properties of Cartesian and infinite products of chaotic attractors. Key results include decompositions of tangent spaces, Hilbert space embeddings, compatibility of smooth and Riemannian structures, stability and Lyapunov exponent criteria for product flows, and the triviality of tangent bundles in both finite and infinite settings.