Invariant Distributions and local theory of quasiperiodic cocycles in $\mathbb{T} ^{d} \times SU(2)$}
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Supporting information
Author(s)
Karaliolios, N
Type
Journal Article
Abstract
We prove local genericity of Distributional Unique Ergodicity (DUE) for certain classes of quasiperiodic cocycles in $\mathbb{T} ^{d} \times SU(2)$, extending and/or refining some preceding results in the field. The proof is based on a more careful analysis of the K.A.M. scheme of [Kri99] and [Kar13], inspired from [Eli02], which also gives a proof of the local density of cocycles which are reducible via finitely differentiable or measurable tranfer functions. We then derive some consequences for one-frequency cocycles over recurrent Diophantine rotations thus confirming in this context (and, therefore, in a manifold of dimension $4$) a conjecture of A. Katok concerning spaces that carry DUE and cohomologically stable diffeomorphisms.
Identifier
http://arxiv.org/abs/1407.4763v4
Subjects
math.DS
Primary 37C55
Notes
37 pages