4 papers
Rigorous numerics for critical orbits in the quadratic family
Ali Golmakani, Comlan Edmond Koudjinan, Stefano Luzzatto +1
We develop algorithms and techniques to compute rigorous bounds for finite pieces of orbits of the critical points, for intervals of parameter values, in the quadratic family of on…
V.I. Arnold's "pointwise" KAM Theorem
Luigi Chierchia, Comlan Edmond Koudjinan
We review V.I. Arnold's 1963 celebrated paper \cite{ARV63} {\sl Proof of A.N. Kolmogorov's theorem on the conservation of conditionally periodic motions with a small variation in t…
A KAM Theorem for finitely differentiable Hamiltonian systems
Comlan Edmond Koudjinan
Given , we prove the persistence of a Cantor--family of KAM tori of measure for any non--degenerate nearly integrable Hamiltonian system o…
Quantitative KAM normal forms and sharp measure estimates
Comlan Edmond Koudjinan
It is widespread since the beginning of KAM Theory that, under "sufficiently small" perturbation, of size , apart a set of measure , all the KAM Tori of a non-degener…