Real-analytic AbC constructions on the torus

In this article we demonstrate a way to extend the AbC (approximation by conjugation) method invented by Anosov and Katok from the smooth category to the category of real-analytic diffeomorphisms on the torus. We present a general framework for such constructions and prove several results. In partic...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2019-10, Vol.39 (10), p.2643-2688
Main Authors: BANERJEE, SHILPAK, KUNDE, PHILIPP
Format: Article
Language:English
Subjects:
Conjugation
Isomorphism
Mathematical analysis
Original Article
Toruses
Translations
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Summary:In this article we demonstrate a way to extend the AbC (approximation by conjugation) method invented by Anosov and Katok from the smooth category to the category of real-analytic diffeomorphisms on the torus. We present a general framework for such constructions and prove several results. In particular, we construct minimal but not uniquely ergodic diffeomorphisms and non-standard real-analytic realizations of toral translations.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2017.132