42 citations · 120 across the 8 of their papers we have counts for
9 papers
On the accumulation of separatrices by invariant circles
Anatole Katok, Raphaël Krikorian
Let be a smooth symplectic diffeomorphism of admitting a (non-split) separatrix associated to a hyperbolic fixed point. We prove that if is a perturbation of…
Jean-Christophe Yoccoz and the theory of circle diffeomorphisms
Hakan Eliasson, Bassam Fayad, Raphaël Krikorian
Our aim in this note is to present some of the crucial contributions of Jean-Christophe Yoccoz to the theory of circle diffeomorphisms. We start with a short historical account bef…
Linearization of quasiperiodically forced circle flow beyond Brjuno condition
Raphael Krikorian, Jing Wang, Jiangong You +1
We prove that an analytic quasiperiodically forced circle flow with a not super-Liouvillean base frequency and which is close enough to some constant rotation is rotat…
KAM-tori near an analytic elliptic fixed point
H. Eliasson, B. Fayad, R. Krikorian
We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector $…
Around the stability of KAM-tori
Hakan Eliasson, Bassam Fayad, Raphaël Krikorian
We show that an analytic invariant torus $\cT_0$ with Diophantine frequency is never isolated due to the following alternative. If the Birkhoff normal form of the Hamiltonian…
Monotonic cocycles
Artur Avila, Raphaël Krikorian
We develop a "local theory" of multidimensional quasiperiodic $\SL(2,\R)$ cocycles which are not homotopic to a constant. It describes a -open neighborhood of cocycles of rota…
A KAM scheme for SL(2,R) cocycles with Liouvillean frequencies
Artur Avila, Bassam Fayad, Raphael Krikorian
We develop a new KAM scheme that applies to SL(2,R) cocycles with one frequency, irrespective of any Diophantine condition on the base dynamics. It gives a generalization of Dinabu…
Reducibility, differentiable rigidity and Lyapunov exponents for quasi-periodic cocycles on
Raphaël Krikorian
Given in some set of total (Haar) measure in , and which is homotopic to the identity, we prove that if th…
Reducibility or non-uniform hyperbolicity for quasiperiodic Schrodinger cocycles
Artur Avila, Raphael Krikorian
We show that for almost every frequency alpha \in \R \setminus \Q, for every C^omega potential v:\R/\Z \to R, and for almost every energy E the corresponding quasiperiodic Schrodin…