Caracterização de uma transição de fase contínua em um sistema caótico

Abstract

We discuss a scaling invariance for chaotic diffusion in a transition from integrabilityto nonintegrability in a class of dynamical systems described by a two-dimensional, nonlinear,and area-preserving mapping. The variables describing the system are the action I and the angle θ, which have the property of diverging in the limit of vanishingly action. The phase transition is controlled by a parameter ϵ. A scaling invariance observed for the average squared action along the chaotic sea proves that the transition observed from integrability to nonintegrability is equivalent to a second order and is therefore called a continuous phase transition. A clear signature of this is to the fact that the order parameter approaches zero simultaneously, and the response of the order parameter to the variation of the control parameter (susceptibility) diverges.