Autori: G. Gentile, V. Mastropietro
Titolo: Methods for the analysisof the Lindstedt series for KAM
tori and renormalizability in classical mechanics.
A review with some applications
This paper consists in a unified exposition of methods and
techniques of the renormalization group approach to quantum
field theory applied to classical mechanics, and in a review
of results:
(1) a proof of the KAM theorem, by studing the perturbative
expansion (Lindstedt series) for the formal solution of the
equations of motion;
(2) a proof of a conjecture by Gallavotti about the
renormalizability of isochronous hamiltonians, i.e. the
possibility to add a term depending only on the actions in a
hamiltonian function not verifying the anisochrony condition
so that the resulting hamiltonian is integrable.
Such results were obtained first by Eliasson; however the
difficulties arising in the study of the perturbative series
are very similar to the problems which one has to deal with in
quantum field theory, so that the use the methods which have
been envisaged and developed in the last twenty years exactly
in order to solve them allows us to obtain unified proofs,
both conceptually and technically.
In the final part of the review, the original work of Eliasson
is analyzed and exposed in detail; its connection with other
proofs of the KAM theorem based on his method is elucidated.
Indirizzi:
Guido Gentile IHES, 35 Route de Chartres, 91440 Bures sur
Yvette, France. e-mail: gentileg%39943.hepnet@lbl.gov.
Vieri Mastropietro Dipartimento di Matematica, Universita' di
Roma II "Tor Vergata", 00133 Roma, Italia.