JournalsjemsVol. 24, No. 8pp. 2605–2690

Measure preserving diffeomorphisms of the torus are unclassifiable

  • Matthew Foreman

    University of California, Irvine, USA
  • Benjamin Weiss

    Hebrew University of Jerusalem, Israel
Measure preserving diffeomorphisms of the torus are unclassifiable cover
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Abstract

In 1932 von Neumann proposed classifying the statistical behavior of differentiable systems. In modern language this is interpreted as classifying diffeomorphisms of compact manifolds up to measure isomorphism. This paper proves that this is impossible in a rigorous sense.

Cite this article

Matthew Foreman, Benjamin Weiss, Measure preserving diffeomorphisms of the torus are unclassifiable. J. Eur. Math. Soc. 24 (2022), no. 8, pp. 2605–2690

DOI 10.4171/JEMS/1151