Statistical approach to nonhyperbolic chaotic systems

Spectral properties of the evolution operator For probability densities are obtained for unimodal maps for which all periodic orbits are unstable, and the Lyapunov exponent calculated from the first iterate or the critical point converges to a positive constant. The method is applied to the logistic map both for parameter values at which finite Markov partitions can be found as well as For more typical parameter values. A universal behavior is found for the spectral gap in the period-doubling inverse cascade of chaotic band-merging bifurcations. Full agreement with numerical simulation is obtained.