Claire Chavaudret
Reducibility of cocycles under a Brjuno-R\"ussmann arithmetical condition.
Втр, 07/26/2011 - 15:01 — SomNambulAuthors: Stefano Marmi, Claire Chavaudret
Subjects: Dynamical Systems
AbstractThe arithmetics of the frequency and of the rotation number play a fun-
damental role in the study of reducibility of analytic quasi-periodic cocycles
which are sufficiently close to a constant. In this paper we show how to
generalize previous works by L.H.Eliasson which deal with the diophantine case
so as to implement a Brjuno-Russmann arithmetical condition both on the
frequency and on the rotation number. Our approach adapts the Poschel-Russmann
KAM method, which was previously used in the problem of linearization of vector
fields, to the problem of reducing cocycles.Presque r\'eductibilit\'e des cocycles quasi-p\'eriodiques de classe Gevrey 2.
Ср, 01/13/2010 - 16:01 — SomNambulAuthors: Claire Chavaudret
Subjects: Dynamical Systems
AbstractGevrey 2 quasi-periodic cocycles with diophantine frequency, close to a
constant, with values in classical Lie groups, are almost reducible in a weak
sense. This is the analogue of Eliasson's almost reducibility theorem for
analytic cocycles.Almost reducibility of analytic quasi-periodic cocycles.
Пт, 12/25/2009 - 16:01 — SomNambulAuthors: Claire Chavaudret
Subjects: Dynamical Systems
AbstractLet $G\subset GL(n,\mathbb{C})$ a classical Lie group, $\mathcal{G}$ the Lie
algebra associated to $G$, $\omega\in \mathbb{R}^d$ a diophantine vector, $A\in
\mathcal{G}$ and a map $F\in C^\omega_r(\mathbb{T}^d,\mathcal{G})$ which is
analytic on a neighbourhood of the torus of radius $r\leq {1/2}$, and $r'\in
]0,r[$. There exists $\epsilon$ depending only on $n,d, A, r-r'$ and on the
diophantine class of $\omega$ such that if $\mid F\mid_r \leq \epsilon$, then
the quasi-periodic cocycle generated by $A+F$ is almost reducible in
$C^\omega_{r'}(2\mathbb{T}^d,G)$.- Читать далее
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