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February  2006, 15(1): 121-142. doi: 10.3934/dcds.2006.15.121

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, France

Received  December 2004 Revised  July 2005 Published  February 2006

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.
Keywords: minimal self-joinings, disjointness, Joinings, weak disjointness, 2-fold and 3-fold mixing..
Mathematics Subject Classification: Primary: 37A05, 37A35; Secondary: 60G1.
Citation: Thierry de la Rue. An introduction to joinings in ergodic theory. Discrete & Continuous Dynamical Systems, 2006, 15 (1) : 121-142. doi: 10.3934/dcds.2006.15.121
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