Statistical properties of dynamical systems - simulation and abstract computation.
Identifieur interne : 001C52 ( Main/Exploration ); précédent : 001C51; suivant : 001C53Statistical properties of dynamical systems - simulation and abstract computation.
Auteurs : Stefano Galatolo [Italie] ; Mathieu Hoyrup [France] ; Cristobal Rojas [Chili]Source :
- Chaos, Solitons and Fractals [ 0960-0779 ] ; 2012-01-01.
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).
Url:
DOI: 10.1016/j.chaos.2011.09.011
Affiliations:
- Chili, France, Italie
- Grand Est, Lorraine (région), Toscane
- Metz, Nancy, Pise
- Université de Lorraine, Université de Pise
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Le document en format XML
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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).</div></front></TEI><affiliations><list><country><li>Chili</li><li>France</li><li>Italie</li></country><region><li>Grand Est</li><li>Lorraine (région)</li><li>Toscane</li></region><settlement><li>Metz</li><li>Nancy</li><li>Pise</li></settlement><orgName><li>Université de Lorraine</li><li>Université de Pise</li></orgName></list><tree><country name="Italie"><region name="Toscane"><name sortKey="Galatolo, Stefano" sort="Galatolo, Stefano" uniqKey="Galatolo S" first="Stefano" last="Galatolo">Stefano Galatolo</name></region></country><country name="France"><region name="Grand Est"><name sortKey="Hoyrup, Mathieu" sort="Hoyrup, Mathieu" uniqKey="Hoyrup M" first="Mathieu" last="Hoyrup">Mathieu Hoyrup</name></region></country><country name="Chili"><noRegion><name sortKey="Rojas, Cristobal" sort="Rojas, Cristobal" uniqKey="Rojas C" first="Cristobal" last="Rojas">Cristobal Rojas</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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