We discuss the dissipative dynamics of a classical particle coupled to an infinite heat reservoir. We announce a number of results concerning the ergodic properties of this model. The novelty of our approach is that it extends beyond Markovian dynamics to the case where the Langevin equation

. We discuss the dissipative dynamics of a classical particle coupled to an infinite heat reservoir. We announce a number of results concerning the ergodic properties of this model. The novelty of our approach is that it extends beyond Markovian dynamics to the case where the Langevin equation

In a recent work [5] various Markov and ergodicity properties of the nonlinear filter, for the classical model of nonlinear filtering, were studied. It was shown that under quite general conditions, when the signal is a Feller-Markov process with values in a complete separable metric space E

In this paper we discuss the ergodic properties of quantum conservative systems by analyzing the behavior of two different models. Despite their intrinsic differencies they both show localization effects in analogy to the dynamical localization found in Kicked Rotator. 1

We show that a stationary IDp process (i.e., an infinitely divisible stationary process without Gaussian part) can be written as the independent sum of four stationary IDp processes, each of them belonging to a different class characterized by its Lévy measure. The ergodic properties of each class

Abstract. For a smooth ZZ2−action on a C ∞ compact Riemannian manifold M, we discuss its ergodic properties which include the decomposition of the tangent space of M into subspaces related to Lyapunov exponents, the existence of Lyapunov charts, and the subaddtivity of entropies. In this paper we

Markov processes describe the time-evolution of random systems that do not have any memory. Let us demonstrate what we mean by this with the following example. Consider a switch that has two states: on and off. At the beginning of the experiment, the switch is on. Every minute after that, we throw a dice. If the dice shows 6, we flip the switch,

Abstract: The problem of the existence of a Strong Stochasticity Threshold in the FPU-β model is reconsidered, using suitable microcanonical observables of thermodynamic nature, like the temperature and the specific heat. Explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry. Measurements of the corresponding temporal autocorrelation functions locate the threshold at a finite value of the energy density, that results to be independent of the number of degrees of freedom.

Abstract. Let T be a bounded linear operator on a Banach space X. We n ∑ T prove some properties of X1 = {z ∈ X: lim n k=1 kz exists} and we con-k struct an operator T such that lim‖T n n /n ‖ = 0, but (I −T)X is not included in X1. 1.

We consider two examples of Viana maps for which the base dynamics has singularities (discontinuities or critical points) and show the existence of a unique absolutely continuous invariant probability measure and related ergodic properties such as stretched exponential decay of correlations