Entropy dimension of measure preserving systems

Measure Preserving Systems

Derivative Formulas for Generalized Srb Measure, Entropy, and Hausdorff Dimension of Hyperbolic Systems of Codimension One

Under the condition that unstable manifolds are one dimensional, the derivative formula of the potential function of the generalized SRB measure with respect to the underlying dynamical system is extended from the hyperbolic attractor case to the general case when the hyperbolic set intersecting with unstable manifolds is a Cantor set. It leads to derivative formulas of objects and quantities t...

Weak disjointness of measure preserving dynamical systems

Two measure preserving dynamical systems are weakly disjoint if some pointwise convergence property is satisfied by ergodic averages on their direct product (a precise definition is given below). Disjointness implies weak disjointness. We start studying this new concept, both by stating some general properties and by giving various examples. The content of the article is summarized in the intro...

Algorithmically random points in measure preserving systems, statistical behaviour, complexity and entropy

We consider the dynamical behavior of Martin-Löf random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computable partitions to define a sort of effective symbolic model for the dynamics. Trough this construction we prove that such points have typical statistical behavior (the behavior which is typical in the Birkhoff ergodic...

Entropy Production in Open Volume–Preserving Systems

We describe a mechanism leading to positive entropy production in volumepreserving systems under nonequilibrium conditions. We consider volumepreserving systems sustaining a diffusion process like the multibaker map or the Lorentz gas. A continuous flux of particles is imposed across the system resulting in a stationary gradient of concentration. In the limit where such flux boundary conditions...