GIBBS MEASURES AND POWER SPECTRA FOR TYPE-I INTERMITTENT MAPS

Gibbs measures of dynamical systems are investigated using the corresponding correlation function and power spectrum. The method is shown to be equivalent to the concept of order-q power spectra which has been developed previously. A technique for the computation of these spectra is presented. As an application we specially focus on the treatment of type I intermittent model maps and investigate their phase transition. In the vicinity of the phase transition point the order-q power spectra are shown to obey some typical scaling relation which is captured neither by the topological pressure nor by the ordinary power spectrum.