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

2001/06/05 by Maria Saprykina, Saprykina, Maria
Mathematics · #37A05 #37A25 #37J40 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:37A05 #msc:37A25 #msc:37J40

paper · pdf · doi:10.48550/arxiv.math/0106032

New corrected version

openalex publication_date 2001/06/05 · arxiv created 2002/06/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the behavior of diffeomorphisms, contained in the closure \A_\a (in the inductive limit topology) of the set \A_\a of real-analytic diffeomorphisms of the torus \Bbb T², conjugated to the rotation R_\a:(x,y)↦ (x + \a, y) by an analytic measure-preserving transformation. We show that for a generic \a∈ [0,1], \A_\a contains a dense set of uniquely ergodic diffeomorphisms. We also prove that \A_\a contains a dense set of diffeomorphisms that are minimal and non-ergodic.

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