2 citations · 3 across the 2 of their papers we have counts for
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V.I. Arnold's "Global" KAM Theorem and geometric measure estimates
L. Chierchia, C. E. Koudjinan
This paper continues the discussion started in [CK19] concerning Arnold's legacy on classical KAM theory and (some of) its modern developments. We prove a detailed and explicit `gl…
Action-angle Variables for Generic 1D Mechanical Systems
Luca Biasco, Luigi Chierchia
We consider a 1D mechanical system in action-angle variable where $\bar {\…
On the measure of KAM tori in two degrees of freedom
Luca Biasco, Luigi Chierchia
A conjecture of Arnold, Kozlov and Neishtadt on the exponentially small measure of the non-torus set in analytic systems with two degrees of freedom is discussed.
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…
On the topology of nearly-integrable Hamiltonians at simple resonances
L. Biasco, L. Chierchia
We show that, in general, averaging at simple resonances a real--analytic, nearly--integrable Hamiltonian, one obtains a one--dimensional system with a cosine--like potential; ``in…
KAM Theory for secondary tori
Luca Biasco, Luigi Chierchia
In [3] (Rend. Lincei Mat. Appl. 26 (2015), 1-10; see also arXiv:1503.08145 [math.DS]) the following result has been announced: Theorem. Consider a real-analytic nearly-integrable m…