Statistical properties of intermittent maps with unbounded derivative

Giampaolo Cristadoro, Nicolai Haydn, Philippe Marie, Sandro Vaienti

Published 2008-12-02, updated 2008-12-16Version 2

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 H\"older continuous observables. We moreover show that the return and hitting times are in the limit exponentially distributed.