Random-like properties of chaotic forcing

Matteo Tanzi (NYU)
Abstract

To which extent a deterministic chaotic system resembles a random process? This is one of the main questions in the study of dynamical systems and it has been addressed in various contexts and from different points of view. In this talk, I will discuss some similarities between randomly driven systems and systems driven by highly chaotic deterministic forcing. More precisely, I will present a result proving that the latter share some of the properties of random ergodic Markov chains modulo controlled errors. For example, they exhibit approximate exponential decay of correlations, meaning that the exponential rate is observed within a given finite resolution. Most importantly, the errors can be made arbitrarily small by increasing the “chaoticity" of the forcing.