A simple system presenting Noise Induced Order

In this talk I will present a family of one dimensional systems with random additive noise such that, as the noise size increases, the Lyapunov exponent of the stationary measure transitions from positive to negative. This phenomena is known in literature as Noise Induced Order, and was first observed in a model of the Belosouv-Zhabotinsky reaction and its existence was proven only recently by Galatolo-Monge-Nisoli. In the talk I will show how this phenomena is strictly connected with non-uniform hyperbolicity and the coexistence of regions of expansion and contraction in phase space; the result is attained through a result on the continuity of the Lyapunov exponent of the stationary measure with respect to the size of the noise.