Real-analytic AbC constructions on the torus

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 nonstandard real-analytic realizations of toral translations.

48 pages, 7 figures

References in corpus (1)

• Non-standard real-analytic realizations of some rotations of the circle

Cited by in corpus (3)

• A question of Norton-Sullivan in the analytic case
• Real-analytic diffeomorphisms with homogeneous spectrum and disjointness of convolutions
• Godel Diffeomorphisms