We show that multiple polynomial ergodic averages arising from nilpo-tent groups of measure preserving transformations of a probability space always converge in the L 2 norm.

We consider classes of partially hyperbolic diffeomorphism f : M → M with splitting TM = Es ⊕ Ec ⊕ Eu and dim Ec = 2. These classes include for instance (perturbations of) the product of Anosov and conservative surface ...

In a previous paper we have given a general framework for addressing the definition of quantum chaos by identifying the conditions that a quantum system must satisfy to lead to non-integrability in its classical limit. ...

We consider a kinetic Ising model which represents a generic agent-based model for various types of socio-economic systems. We study the case of a finite (and not necessarily large) number of agents N as well as the ...

This paper studies recursive exchange economies with short sales. Agents maximize discounted expected utility. The asset structure is general and includes real securities, infinite-lived stocks, options, and other derivatives. ...

We consider different ergodic averages and estimate the measure of the set of points in which the averages apart from a given value. The cases considered are empirical measures of cylinders in symbolic spaces and averages ...

We prove some criteria for uniform hyperbolicity based on the periodic points of the transformation. More precisely, if a mild hyperbolicity condition holds for the periodic points of any diffeomorphism in a residual subset ...

We study the a.e. convergence of the Cesàro-$(1+\alpha)$ ergodic averages and the a.e. existence in the Cesàro-$\alpha$ sense of the ergodic Hilbert transform associated with Cesàro bounded flow and $-1\lt \alpha \leq 0$.