11 papers
Optimal linearization of vector fields on the torus in non-analytic Gevrey classes
Abed Bounemoura
We study linear and non-linear small divisors problems in analytic and non-analytic regularity. We observe that the Bruno arithmetic condition, which is usually attached to non-lin…
Some remarks on the Classical KAM Theorem, following P{ö}schel
Abed Bounemoura
We propose a slight correction and a slight improvement on the main result contained in "A lecture on Classical KAM Theorem" by J. P{ö}schel.
Reducibility of ultra-differentiable quasi-periodic cocycles under an adapted arithmetic condition
Abed Bounemoura, Claire Chavaudret, Shuqing Liang
We prove a reducibility result for sl(2,R) quasi-periodic cocycles close to a constant elliptic matrix in ultra-differentiable classes, under an adapted arithmetic condition which…
Positive measure of KAM tori for finitely differentiable Hamiltonians
Abed Bounemoura
Consider an integer and real numbers and . Using ideas of Moser, Salamon proved that individual Diophantine tori persist for Hamiltonian systems which…
Some remarks on the optimality of the Bruno-R{ü}ssmann condition
Abed Bounemoura
We prove that the Bruno-R{ü}ssmann condition is optimal for the analytic preservation of a quasi-periodic invariant curve for an analytic twist map. The proof is based on Yoccoz's…
Hamiltonian perturbation theory for ultra-differentiable functions
Abed Bounemoura, Jacques Féjoz
Some scales of spaces of ultra-differentiable functions are introduced, having good stability properties with respect to infinitely many derivatives and compositions. They are well…