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An example of non-coincidence of minimal and statistical attractors

Published online by Cambridge University Press:  24 March 2006

V. KLEPTSYN
V. KLEPTSYN
Affiliation:
Section de Mathématiques, Université Genève, 2–4 rue du Lièvre, 1211 CP 64, Genève, Suisse UMPA (UMR 5669 CNRS), École Normale Supérieure de Lyon, 46 allée d'Italie, 69007, Lyon, France Independent University of Moscow, 11 Bol'shoj Vlas'evski per., 119002, Moscow, Russia Moscow State University, Department of Mechanics and Mathematics, Vorob'evy Gory, 119992, Moscow, Russia (e-mail: [email protected])
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Abstract

In this work we construct an example of a smooth dynamical system for which the minimal and statistical attractors do not coincide. In the language of SRB measures, this is an example for which there exists a unique natural measure, but there is no observable one. Also, as the statistical attractor describes the mean behaviour of individual points, and the minimal one the mean behaviour of the Lebesgue measure, this example provides us with a dynamical realization of the Riesz example.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 3 , June 2006 , pp. 759 - 768
Copyright
2006 Cambridge University Press

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