An introduction to joinings in ergodic theory

Abstract

Since their introduction by Furstenberg in 1967, 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 on - 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.