An ergodic system is dominant exactly when it has positive entropy

Tim Austin, Eli Glasner, Jean Paul Thouvenot, Benjamin Weiss

Research output: Contribution to journalArticlepeer-review


An ergodic dynamical system is called dominant if it is isomorphic to a generic extension of itself. It was shown by Glasner et al [On some generic classes of ergodic measure preserving transformations. Trans. Moscow Math. Soc. 82(1) (2021), 15-36] that Bernoulli systems with finite entropy are dominant. In this work, we show first that every ergodic system with positive entropy is dominant, and then that if has zero entropy, then it is not dominant.

Original languageEnglish
Pages (from-to)3216-3230
Number of pages15
JournalErgodic Theory and Dynamical Systems
Issue number10
StatePublished - 4 Oct 2023


  • Bernoulli systems
  • dominant systems
  • generic properties
  • relative Bernoulli
  • very weak Bernoulli


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