Abstract
We construct on any smooth compact connected manifold of dimension greater than two on which there exists an effective smooth circle action preserving a positive smooth volume an uncountable family of smooth ergodic zero-entropy diffeomorphisms that are pairwise non-Kakutani equivalent. We first construct a smooth ergodic zero-entropy and non-loosely Bernoulli diffeomorphism by suitably modifying a smooth construction by Anosov and Katok.
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Benhenda, M. An uncountable family of pairwise non-Kakutani equivalent smooth diffeomorphisms. JAMA 127, 129–178 (2015). https://doi.org/10.1007/s11854-015-0027-z
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DOI: https://doi.org/10.1007/s11854-015-0027-z