Scaling Behaviors of Characteristic Exponents near Chaotic Transition Points

Abstract

Characteristic exponents, which have been introduced previously for extended Lyapunov exponents, are studied for the system Xt+1=Xt+pr(Xt), (pr(X+1)=pr(X)), near its transition points of chaos-induced diffusion. The scaling properties of the characteristic exponents are discovered and turn out to depend on the types of the transition points. For two typical cases, explicit forms of scaling functions are analytically determined. The numerical calculations of the characteristic exponents for the sinusoidal map pr(X)=rsin (2πX) are carried out, and a good agreement with the analytical results is obtained.