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math.DS2019
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.
math.DS2019★ 7 cited
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…
math.DS2019★ 7 cited
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…