167 citations · 212 across the 17 of their papers we have counts for
18 papers
Singular KAM theory for convex Hamiltonian systems
Santiago Barbieri, Luca Biasco, Luigi Chierchia +1
In this note, we briefly discuss how singular KAM Theory - which was worked out in a previous work by L.B. and L.C. for the mechanical case - can b…
Singular KAM Theory
Luca Biasco, Luigi Chierchia
The question of the total measure of invariant tori in analytic, nearly--integrable Hamiltonian systems is considered. In 1985, Arnol'd, Kozlov and Neishtadt, in the Encyclopaedia…
Global properties of generic real-analytic nearly-integrable Hamiltonian systems
Luca Biasco, Luigi Chierchia
We introduce a new class of generic real analytic potentials on and study global analytic properties of natural nearly-integrable Hamiltonians $\fra…
Complex Arnol'd-Liouville maps
Luca Biasco, Luigi Chierchia
We discuss the holomorphic properties of the complex continuation of the classical Arnol'd-Liouville action-angle variables for real analytic 1 degree--of--freedom Hamiltonian syst…
Quasi-periodic motions in generic nearly-integrable mechanical systems
Luca Biasco, Luigi Chierchia
In this note we present and briefly discuss results, which include as a particular case the theorem announced in [L. Biasco, and L. Chierchia. On the measure of Lagrangian invarian…
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…