Abstract
This paper is the first of a series of papers culminating in the result that measure preserving diffeomorphisms of the disc or 2-torus are unclassifiable. It addresses another classical problem: which abstract measure preserving systems are realizable as smooth diffeomorphisms of a compact manifold? The main result gives symbolic representations of Anosov–Katok diffeomorphisms.
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The first author would like to acknowledge partial support under NSF award DMS 07010310
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Foreman, M., Weiss, B. A symbolic representation for Anosov–Katok systems. JAMA 137, 603–661 (2019). https://doi.org/10.1007/s11854-019-0010-1
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DOI: https://doi.org/10.1007/s11854-019-0010-1