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Aspects of Lagrange's Mechanics and their Legacy
Giovanni Gallavotti
From the "vibrating string" and "Kepler's equation" theories to relativistic quantum fields, perturbation theory, (divergent) series resummations, KAM theory.
Borel summability and Lindstedt series
O. Costin, G. Gallavotti, G. Gentile +1
Resonant motions of integrable systems subject to perturbations may continue to exist and to cover surfaces with parametric equations admitting a formal power expansion in the stre…
Constructive Quantum Field Theory
Giovanni Gallavotti
A review of the renormalization group approach to the proof of non perturbative ultraviolet stability in scalar field theories in dimension d=2,3.
Fractional Lindstedt series
Giovanni Gallavotti, Guido Gentile, Alessandro Giuliani
The parametric equations of the surfaces on which highly resonant quasi-periodic motions develop (lower-dimensional tori) cannot be analytically continued, in general, in the pertu…
CKN theory of singularities of weak solutions of the Navier-Stokes equations
Giovanni Gallavotti
The lectures are devoted to a complete exposition of the theory of singularities of the Navier Stokes equations solution studied by Leray, in a simple geometrical setting in which…
Hyperbolic low-dimensional invariant tori and summations of divergent series
G. Gallavotti, G. Gentile
We consider a class of a priori stable quasi-integrable analytic Hamiltonian systems and study the regularity of low-dimensional hyperbolic invariant tori as functions of the pertu…