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math.DS2013★ 42 cited
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…
math.DS2013
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…