23 citations · 116 across the 28 of their papers we have counts for
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math.DS2012★ 10 cited
Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians
Abed Bounemoura
This paper is a sequel to "Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with a…
math.DS2012★ 13 cited
Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians
Abed Bounemoura
In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based…
math.DS2012
A Diophantine duality applied to the KAM and Nekhoroshev theorems
Abed Bounemoura, Stephane Fischler
In this paper, we use geometry of numbers to relate two dual Diophantine problems. This allows us to focus on simultaneous approximations rather than small linear forms. As a conse…