Statistical properties of intermittent maps with unbounded derivative

Abstract

We study the ergodic and statistical properties of a class of maps of the circle and of the interval of Lorenz type which present indifferent fixed points and points with unbounded derivative. These maps have been previously investigated in the physics literature. We prove in particular that correlations decay polynomially, and that suitable limit theorems (convergence to stable laws or central limit theorem) hold for Hölder continuous observables. Moreover, we show that the return and hitting times are exponentially distributed in the limit.