Differentiable rigidity for quasiperiodic cocycles in compact Lie groups
File(s)
Accepted version
Author(s)
Karaliolios, N
Type
Journal Article
Abstract
We study close-to-constants quasiperiodic cocycles in $\mathbb{T} ^{d} \times
G$, where $d \in \mathbb{N} ^{*} $ and $G$ is a compact Lie group, under the
assumption that the rotation in the basis satisfies a Diophantine condition. We
prove differentiable rigidity for such cocycles: if such a cocycle is
measurably conjugate to a constant one satisfying a Diophantine condition with
respect to the rotation, then it is $C^{\infty}$-conjugate to it, and the
K.A.M. scheme actually produces a conjugation. We also derive a global
differentiable rigidity theorem, assuming the convergence of the
renormalization scheme for such dynamical systems.
G$, where $d \in \mathbb{N} ^{*} $ and $G$ is a compact Lie group, under the
assumption that the rotation in the basis satisfies a Diophantine condition. We
prove differentiable rigidity for such cocycles: if such a cocycle is
measurably conjugate to a constant one satisfying a Diophantine condition with
respect to the rotation, then it is $C^{\infty}$-conjugate to it, and the
K.A.M. scheme actually produces a conjugation. We also derive a global
differentiable rigidity theorem, assuming the convergence of the
renormalization scheme for such dynamical systems.
Date Issued
2017-01-01
Date Acceptance
2016-06-04
Citation
Journal of Modern Dynamics, 2017, 11, pp.125-142
ISSN
1930-532X
Publisher
American Institute of Mathematical Sciences
Start Page
125
End Page
142
Journal / Book Title
Journal of Modern Dynamics
Volume
11
Copyright Statement
© American Institute of Mathematical Sciences
Identifier
http://arxiv.org/abs/1407.4799v3
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Rigidity
quasi-periodic cocycles
compact Lie groups
KAM theory
REDUCIBILITY
math.DS
37C55
0101 Pure Mathematics
Publication Status
Published