Scaling structures of fluctuation spectra near chaotic transition points

Abstract

The symmetry dynamics and the fluctuation dynamics for local expansion rates are investigated in the vicinity of two kinds of intermittency transition points. This is done with the aid of the characteristic function ${\lambda }_q$ and the fluctuation spectrum σ(α) describing the global characteristics of time series. In both cases they obey the scaling laws ${\lambda }_q$=${\epsilon }^{\mu }$L(q/${\epsilon }^{\nu }$) and σ(α)=${\epsilon }^{\mu +\nu }$S(α/${\epsilon }^{\mu }$), where ε is the deviation from the transition point, and L and S are the scaling functions, μ and ν being constants.