Approximation of stationary statistical properties of dissipative dynamical systems: Time discretization

Approximation of stationary statistical properties of dissipative dynamical systems: Time discretization

We consider temporal approximation of stationary statistical properties of dissipative complex dynamical systems. We demonstrate that stationary statistical properties of the time discrete approximations (numerical scheme) converge to those of the underlying continuous dissipative complex dynamical system under three very natural assumptions as the time step approaches zero. The three condition...

Numerical algorithms for stationary statistical properties of dissipative dynamical systems

It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. The main concern of this manuscript is numerical methods for dissipative chaotic infinite dimensional dynamical systems that are able to capture the stationary statistical properties of the underlying dynamical systems. We first survey results on temporal and spatial approximations that enjoy the...

Upper Semi-continuity of Stationary Statistical Properties of Dissipative Systems

We show that stationary statistical properties for uniformly dissipative dynamical systems are upper semi-continuous under regular perturbation and a special type of singular perturbation in time of relaxation type. The results presented are applicable to many physical systems such as the singular limit of infinite Prandtl-Darcy number in the Darcy-Boussinesq system for convection in porous med...

Statistical Properties of Nonequilibrium Dynamical Systems

We provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our work covers systems that admit a finite SRB measure and it also covers systems that admit an infinite SRB measure. In particular, we obtain a linear response formula for both finite and infinite SRB measures. We apply our results to interval maps with a neutral fixed p...

On Statistical Properties of Dynamical Systems