Corpus ID: 119733273

# Invariant Distributions and local theory of quasiperiodic cocycles in $\mathbb{T} ^{d} \times SU(2)$}

@article{Karaliolios2014InvariantDA,
title={Invariant Distributions and local theory of quasiperiodic cocycles in \$\mathbb\{T\} ^\{d\} \times SU(2)\$\}},
author={Nikolaos Karaliolios},
journal={arXiv: Dynamical Systems},
year={2014}
}
We study the linear cohomological equation in the smooth category over quasi-periodic cocycles in $\mathbb{T} ^{d} \times SU(2)$. We prove that, under a full measure condition on the rotation in $\mathbb{T} ^{d}$, for a generic cocycle in an open set of cocycles, the equation admits a solution for a dense set of functions on $\mathbb{T} ^{d} \times SU(2)$ of zero average with respect to the Haar measure. This property is known as Distributional Unique Ergodicity (DUE). We then show that given… Expand
2 Citations
Continuous Spectrum or Measurable Reducibility for Quasiperiodic Cocycles in $${\mathbb{T} ^{d} \times SU(2)}$$Td×SU(2)
AbstractWe continue our study of the local theory for quasiperiodic cocycles in $${\mathbb{T} ^{d} \times G}$$Td×G , where $${G=SU(2)}$$G=SU(2) , over a rotation satisfying a Diophantine conditionExpand
Fibered rotation vector and hypoellipticity for quasi‐periodic cocycles in compact Lie groups
Using weak solutions to the conjugation equation, we define a fibered rotation vector for almost reducible quasi-periodic cocycles in $\mathbb{T}^{d} \times G$, $G$ a compact Lie group, over aExpand

#### References

SHOWING 1-10 OF 27 REFERENCES
Global aspects of the reducibility of quasiperiodic cocycles in semisimple compact Lie groups
In this PhD thesis we study quasiperiodic cocycles in semi-simple compact Lie groups. For the greatest part of our study, we will focus ourselves to one-frequency cocyles. We will prove thatExpand
Rigidity results for quasiperiodic SL(2, R) -cocycles
• Mathematics
• 2010
In this paper we introduce a new technique that allows us to investigate reducibility properties of smooth SL(2, R)-cocycles over irrational rotations of the circle beyond the usual DiophantineExpand
Rigidity of the Reducibility of Gevrey Quasi-periodic Cocycles on U(n)
• Mathematics
• 2013
We consider the reducibility problem of cocycles $(\alpha,A)$ on $\T^d\times U(n)$ in Gevrey classes, where $\alpha$ is a Diophantine vector. We prove that, if a Gevrey cocycle is conjugated to aExpand
On the degree of cocycles with values in the groupSU(2)
AbstractIn this paper are presented some properties of smooth cocycles over irrational rotations on the circle with values in the groupSU(2). It is proved that the degree of anyC2-cocycle (the notionExpand
Ergodic skew-systems on \mathbb{T}^d \times SO(3,\mathbb{R}}
• L. Eliasson
• Mathematics
• Ergodic Theory and Dynamical Systems
• 2002
Analytic quasi-periodic skew-systems with close to constant coefficients and with Diophantine frequencies seem to be, in a measure theoretical sense, ‘generically’ reducible. In this paper we showExpand
Almost reducibility for finitely differentiable SL(2,R)-valued quasi-periodic cocycles
Quasi-periodic cocycles with a diophantine frequency and with values in SL(2,R) are shown to be almost reducible as long as they are close enough to a constant, in the topology of k timesExpand
Cocycles, cohomology and combinatorial constructions in ergodic theory
Cocycles and cohomological equations play a central role in ergodic theory as well as in its applications to other areas of dynamics. Among the questions which are reduced to cohomologicalExpand
Global density of reducible quasi-periodic cocycles on T x SU(2)
We prove that given a in a set of total (Haar) measure in T 1 = R/Z, the set of A ∈ C ∞ (T 1 , SU(2)) for which the skew-product system (α, A): T 1 × SU(2) → T 1 × SU(2), (α, A)(θ,y) = (θ + α, A(θ)y)Expand
Strong almost reducibility for analytic and Gevrey quasi-periodic cocycles
This paper is about almost reducibility of quasi-periodic cocycles with a diophantine frequency which are sufficiently close to a constant. Generalizing previous works by L.H.Eliasson, we show aExpand
A course in abstract harmonic analysis
Banach Algebras and Spectral Theory Banach Algebras: Basic Concepts Gelfand Theory Nonunital Banach Algebras The Spectral Theorem Spectral Theory of *-Representations Von Neumann Algebras Notes andExpand