Effective symbolic dynamics, random points, statistical behavior, complexity and entropy
Identifieur interne : 002E97 ( Main/Exploration ); précédent : 002E96; suivant : 002E98Effective symbolic dynamics, random points, statistical behavior, complexity and entropy
Auteurs : Stefano Galatolo [Italie] ; Mathieu Hoyrup [France] ; Cristobal Rojas [Canada]Source :
- Information and Computation [ 0890-5401 ] ; 2010.
English descriptors
- mix :
Abstract
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. Through this construction we prove that such points have typical statistical behavior (the behavior which is typical in the Birkhoff ergodic theorem) and are recurrent. We introduce and compare some notions of complexity for orbits in dynamical systems and prove: (i) that the complexity of the orbits of random points equals the Kolmogorov-Sinaï entropy of the system, (ii) that the supremum of the complexity of orbits equals the topological entropy.
Url:
DOI: 10.1016/j.ic.2009.05.001
Affiliations:
- Canada, France, Italie
- Grand Est, Lorraine (région), Ontario, Toscane
- Metz, Nancy, Pise, Toronto
- Université de Lorraine, Université de Pise, Université de Toronto
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Le document en format XML
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We use computable partitions to define a sort of effective symbolic model for the dynamics. Through this construction we prove that such points have typical statistical behavior (the behavior which is typical in the Birkhoff ergodic theorem) and are recurrent. We introduce and compare some notions of complexity for orbits in dynamical systems and prove: (i) that the complexity of the orbits of random points equals the Kolmogorov-Sinaï entropy of the system, (ii) that the supremum of the complexity of orbits equals the topological entropy.</div></front></TEI><affiliations><list><country><li>Canada</li><li>France</li><li>Italie</li></country><region><li>Grand Est</li><li>Lorraine (région)</li><li>Ontario</li><li>Toscane</li></region><settlement><li>Metz</li><li>Nancy</li><li>Pise</li><li>Toronto</li></settlement><orgName><li>Université de Lorraine</li><li>Université de Pise</li><li>Université de Toronto</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="Canada"><region name="Ontario"><name sortKey="Rojas, Cristobal" sort="Rojas, Cristobal" uniqKey="Rojas C" first="Cristobal" last="Rojas">Cristobal Rojas</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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