An introduction to joinings in ergodic theory

Thierry de la Rue

doi:10.3934/dcds.2006.15.121

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2006, Volume 15, Issue 1: 121-142. Doi: 10.3934/dcds.2006.15.121

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An introduction to joinings in ergodic theory

Thierry de la Rue^1,

1.
Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, CNRS, Avenue de l'Université, Avenue de l'Université, 76801 Saint Étienne du Rouvray

Received: November 30, 2004

Revised: June 30, 2005

Published: February 2006

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Abstract

Since their introduction by Furstenberg [3], joinings have proved a very powerful tool in ergodic theory. We present here some aspects of the use of joinings in the study of measurable dynamical systems, emphasizing

the links between the existence of a non trivial common factor and the existence of a joining which is not the product measure,
how joinings can be employed to provide elegant proofs of classical results,
how joinings are involved in important questions of ergodic theory, such as pointwise convergence or Rohlin's multiple mixing problem.

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Mathematics Subject Classification: Primary: 37A05, 37A35; Secondary: 60G10.

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