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Real-analytic AbC constructions on the torus

Published online by Cambridge University Press:  25 January 2018

SHILPAK BANERJEE  and
PHILIPP KUNDE
SHILPAK BANERJEE
Affiliation:
The Pennsylvania State University, Department of Mathematics, University Park, PA 16802, USA email banerjee.shilpak@gmail.com
PHILIPP KUNDE
Affiliation:
University of Hamburg, Mathematics, Bundesstrasse 55, Hamburg 20146, Germany email philipp.kunde@math.uni-hamburg.de
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Abstract

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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 10 , October 2019 , pp. 2643 - 2688
Copyright
© Cambridge University Press, 2018 

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