Analytic non-linearizable uniquely ergodic diffeomorphisms on the two-torus

Details Analytic non-linearizable uniquely ergodic diffeomorphisms on the two-torus Analytic non-linearizable uniquely ergodic diffeomorphisms on the two-torus

2001-06-05

arxiv.org/abs/math/0106032v2

Mathematics

Dynamical Systems

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Scientific paper

We study the behavior of diffeomorphisms, contained in the closure $\bar {\A_\a}$ (in the inductive limit topology) of the set $\A_\a$ of real-analytic diffeomorphisms of the torus $\Bbb T^2$, conjugated to the rotation $R_\a:(x,y)\mapsto (x + \a, y)$ by an analytic measure-preserving transformation. We show that for a generic $\a\in [0,1]$, $\bar {\A_\a}$ contains a dense set of uniquely ergodic diffeomorphisms. We also prove that $\bar {\A_\a}$ contains a dense set of diffeomorphisms that are minimal and non-ergodic.

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