Statistical properties of dynamical systems - simulation and abstract computation. - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Chaos, Solitons & Fractals Year : 2012

Statistical properties of dynamical systems - simulation and abstract computation.

Abstract

We survey an area of recent development, relating dynamics to theoretical computer science. We discuss some aspects of the theoretical simulation and computation of the long term behavior of dynamical systems. We will focus on the statistical limiting behavior and invariant measures. We present a general method allowing the algorithmic approximation at any given accuracy of invariant measures. The method can be applied in many interesting cases, as we shall explain. On the other hand, we exhibit some examples where the algorithmic approximation of invariant measures is not possible. We also explain how it is possible to compute the speed of convergence of ergodic averages (when the system is known exactly) and how this entails the computation of arbitrarily good approximations of points of the space having typical statistical behaviour (a sort of constructive version of the pointwise ergodic theorem).
Fichier principal
Vignette du fichier
CSF.pdf (500.46 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-00644790 , version 1 (25-11-2011)

Identifiers

Cite

Stefano Galatolo, Mathieu Hoyrup, Cristobal Rojas. Statistical properties of dynamical systems - simulation and abstract computation.. Chaos, Solitons & Fractals, 2012, 45 (1), pp.1-14. ⟨10.1016/j.chaos.2011.09.011⟩. ⟨hal-00644790⟩
242 View
741 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More