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…
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…
Explicit estimates on the measure of primary KAM tori
Luca Biasco, Luigi Chierchia
From KAM Theory it follows that the measure of phase points which do not lie on Diophantine, Lagrangian, "primary" tori in a nearly--integrable, real--analytic Hamiltonian system i…
On the measure of Lagrangian invariant tori in nearly--integrable mechanical systems (draft)
L. Biasco, L. Chierchia
Consider a real--analytic nearly--integrable mechanical system with potential , namely, a Hamiltonian system, having a real-analytic Hamiltonian $$ H(y,x)=\frac12 | y |^2 +\e f(…
The Steep Nekhoroshev's Theorem
Massimiliano Guzzo, Luigi Chierchia, Giancarlo Benettin
Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular,…
The spin-orbit resonances of the Solar system: A mathematical treatment matching physical data
Francesco Antognini, Luigi Chierchia, Luca Biasco
In the mathematical framework of a restricted, slightly dissipative spin-orbit model, we prove the existence of periodic orbits for astronomical parameter values corresponding to a…
Analytic Lagrangian tori for the planetary many-body problem
Luigi Chierchia, Fabio Pusateri
In 2004, Féjoz [Démonstration du 'théoréme d'Arnold' sur la stabilité du système planétaire (d'après M. Herman). Ergod. Th. & Dynam. Sys. 24(5) (2004), 1521-1582], completing inves…
KAM Tori for 1D Nonlinear Wave Equations with Periodic Boundary Conditions
Luigi Chierchia, Jaingong You
In this paper, one-dimensional (1D) nonlinear wave equations , with periodic boundary conditions are considered; V is a periodic smooth or analytic func…
Birth of resonances in the spin-orbit problem of Celestial Mechanics
Alessandra Celletti, Luigi Chierchia
The behaviour of resonances in the spin-orbit coupling in Celestial Mechanics is investigated. We introduce a Hamiltonian nearly-integrable model describing an approximation of the…