Resposta quadrática de sistemas dinâmicos aleatórios e determinísticos = Quadratic response of random and deterministic dynamical systems

Abstract

The present work consists of studying the article Quadratic Response of Random and Deterministic Dynamical Systems [1] which investigates sufficient conditions for the dynamic systems to present a linear response and that, if in addition to such conditions, other conditions were also observed, the system presented, in addition, a quadratic response in its stationary measures. We emphasize that, although the original article also deals with random dynamical systems, the focus of the current work is on the study of deterministic dynamical systems, emphatically on the study of deterministic dynamical systems of expanding maps in the unitary circle, which constitutes a wide range of deterministic dynamical systems and, as we shall see, manifest the desired conditions and therefore exhibit linear and/or quadratic responses in their invariant measures when manifested to small perturbations.