An example of non-coincidence of minimal and statistical attractors

Victor Kleptsyn

HAL: hal-00463760, version 1

An example of non-coincidence of minimal and statistical attractors
Kleptsyn V.
Ergodic Theory and Dynamical Systems 26, 3 (2006) 759-768 - http://hal.archives-ouvertes.fr/hal-00463760

Publication type:

Article in peer-reviewed journal

Subject:

Mathematics/Probability

Title:

An example of non-coincidence of minimal and statistical attractors

Author(s):

Victor Kleptsyn (

) ¹

Laboratory:

1:	Institut de Recherche Mathématique de Rennes (IRMAR)

	http://irmar.univ-rennes1.fr/

	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne

	France

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.

Fulltext language:

English

Journal:

Ergodic Theory and Dynamical Systems
Publisher	Cambridge University Press (CUP)
ISSN	0143-3857 (eISSN : 1469-4417)

Audience:

international

Publication date:

2006

Volume:

Issue:

Page, identifiant, ...:

759-768


hal-00463760, version 1
http://hal.archives-ouvertes.fr/hal-00463760
oai:hal.archives-ouvertes.fr:hal-00463760
From: Maryse Collin <>
Submitted on: Monday, 15 March 2010 09:54:33
Updated on: Monday, 15 March 2010 09:54:33