Parabolic rational maps

We study the dynamics of rational maps with indifferent parabolic points by comparing their dynamical properties to those of it’s ‘jump trans- formation’ which is uniformly expanding on a non-compact set with infinite Markov partition. We establish the spectral properties of a two-variables operator-valued function associated to the jump transformation and exploit their dynamical relevance to study the analytic properties of the pressure, the escape rate from a neighborhood of the Julia set and the asymptotic distribution of pre-images.