Abstract:  Generic properties of measure preserving transformations of the unit interval have been investigated for many years beginning with the work of Halmos and Rokhlin. I will describe a framework for studying the generic properties of an extension of a fixed ergodic transformation. A surprising result is the following dichotomy:
 A generic extension of T is not isomorphic to T if and only if T has zero entropy.

  (joint work with T. Austin, E. Glasner and J-P. Thouvenot)

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