Scaling Behavior of Chaotic Flows

Abstract

It is shown that in the turbulent regime of systems with period-doubling subharmonic bifurcations, the maximum Lyapunov characteristic exponent behaves like $\overline{\lambda }={\overline{\lambda }}_0{(\mathcal{r}-{\mathcal{r}}_c)}^t$, with $t$ a universal exponent which is calculated to be $t=0.449\mathrm{}8069\dots$. This result is in agreement with the available data on $\overline{\lambda }$ for a number of dynamical systems.