A symbolic representation for Anosov–Katok systems
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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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- A.-D. Bjork, Criteria for rank-one transformations to be weakly mixing, and the generating property, Ph. D. dissertation, University of California, Irvine, 2009.Google Scholar
- M. Foreman, D. Rudolph and B. Weiss, Universal models formeasure preserving transformations, preprint.Google Scholar
- M. Foreman and B. Weiss, From odometers to circular systems: A global structure theorem, preprint.Google Scholar
- M. Foreman and B. Weiss, Measure preserving diffeomorphisms of the torus are not classifiable, preprint.Google Scholar
- A. B. Katok and A. M. Stepin, Approximations in ergodic theory, Uspehi Mat. Nauk 22 (1967), no. 5 (137), 81–106.Google Scholar
- K. Petersen, Ergodic Theory, Cambridge Studies in Advanced Mathematics, Vol. 2, Cambridge University Press, Cambridge, 1989, Corrected reprint of the 1983 original.Google Scholar
- P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, Vol. 79, Springer-Verlag, New York–Berlin, 1982.Google Scholar