\begin{thebibliography}{10}

\bibitem{La799}
P.S. Laplace.
\newblock {\em M\'ecanique C\'eleste}.
\newblock reprinted by Chelsea, New York, Paris, 1799.

\bibitem{Po892}
H.~Poincar\'e.
\newblock {\em Les M\'ethodes nouvelles de la M\'ecanique c\'eleste}.
\newblock reprinted by Blanchard, 1987, Paris, 1892.

\bibitem{Ei17}
A.~Einstein.
\newblock Zum quantensatz von {S}ommerfeld und {E}pstein.
\newblock {\em Verhandlungen der Deutschen physikalischen Gesellshaft},
  19:82--02, 1917.

\bibitem{Fe923b}
E.~Fermi.
\newblock Il principio delle adiabatiche e i sistemi che non ammettono
  coordinate angolari.
\newblock {\em Nuovo Cimento}, 25:171--175, 1923.

\bibitem{Si43}
K.~Siegel.
\newblock Iterations of analytic functions.
\newblock {\em Annals of Mathematics}, 43:607--612, 1943.

\bibitem{Ko54}
A.N. Kolmogorov.
\newblock On the preservation of conditionally periodic motions.
\newblock {\em Doklady Akademia Nauk SSSR and Lecture Notes in Physics,
  Stochastic behavior in classical and quantum Hamiltonians, ed. G. Casati, J.
  Ford, Vol. 93, 1979}, 96:527--530, 1954.

\bibitem{Mo55}
C.B. Morrey.
\newblock On the derivation of the equations of hydrodynamics from statistical
  mechanics.
\newblock {\em Communications in Pure and Applied Mathematics}, 8:279--326,
  1955.

\bibitem{He66}
K.~Hepp.
\newblock Proof of the {B}ogoliubov-{P}arasiuk theorem on renmormalization.
\newblock {\em Communications in Mathematical Physics}, 2:301--326, 1966.

\bibitem{WK74}
K.~Wilson and J.~Kogut.
\newblock The renormalization group and the {$\e$}-expansion.
\newblock {\em {\it The renormalization group and the {$\e$}-expansion},
  Physics Reports}, 12:75--199, 1973.

\bibitem{Ga01}
G.~Gallavotti.
\newblock Renormalization group in statistical mechanics and mechanics: gauge
  symmetries and vanishing beta functions.
\newblock {\em Physics Reports}, 352:251--272, 2001.

\bibitem{Fr82b}
J.~Fr{\"o}lich.
\newblock On the triviality of {$\l\f^4_d$} theories and the approach to the
  critical point in {$d\,(\ge4)$} dimensions.
\newblock {\em {\it On the triviality {of $\l\f^4_d$} theories and the approach
  to the critical point in {$d\,(\ge4)$} dimensions}, Nuclear Physics B},
  200:281--296, 1982.

\bibitem{Gr99}
D.J. Gross.
\newblock Twenty five years of asymptotic freedom.
\newblock {\em Nuclear Physics B (Proceedings Supplements))}, 74:426--446,
  1999.

\bibitem{Ne66}
E.~Nelson.
\newblock A quartic interaction in two dimensions.
\newblock {\em {\it A quartic interaction in two dimensions}, In {\sl
  Mathematical Theory of elementary particles}, ed. R Goodman, I. Segal}, pages
  69--73, 1966.

\bibitem{Si74}
B.~Simon.
\newblock {\em The $P(\f)_2$ Euclidean (quantum) field theory}.
\newblock Princeton University PRess, Princeton, 1974.

\bibitem{GJ81}
J.~Glimm and A.~Jaffe.
\newblock {\em Quantum Physics. A functional integral point of view}.
\newblock Springer-Verlag, New York, 1981.

\bibitem{Ga85b}
G.~Gallavotti.
\newblock Renormalization theory and ultraviolet stability for scalar fields
  via renormalization group methods.
\newblock {\em Reviews of Modern Physics}, 57:471--562, 1985.

\bibitem{HV72}
G~{'t} Hooft and MJG Veltman.
\newblock Regularization and renormalization of gauge fields.
\newblock {\em Nuclear Physics B}, 44:189--213, 1972.

\bibitem{Ho99}
G.~'t~Hooft.
\newblock When was asymptotic freedom discovered? or the rehabilitation of
  quantum field theory.
\newblock {\em Nuclear Physics B (Proceedings Supplements)}, 74:413--425, 1999.

\bibitem{Ga85}
G.~Gallavotti.
\newblock Perturbation theory for classical {H}amiltonian systems.
\newblock {\em in {\it Scaling and self similarity in Physics}}, Ed. ed. J.
  Fr{\"o}hlich, Birkhauser, Boston:359--426, 1985.

\bibitem{Ga86}
G.~Gallavotti.
\newblock Quasi integrable mechanical systems.
\newblock {\em Phenom\`enes Critiques, Syst\`emes aleatories, Th\'eories de
  jauge, Proceedings, Les Houches, XLIII (1984)}, II:539--624, 1986.

\bibitem{Po86}
J.~P{\"o}schel.
\newblock Invariant manifolds of complex analytic mappings.
\newblock {\em Phenom\`enes Critiques, Syst\`emes aleatories, Th\'eories de
  jauge, Proceedings, Les Houches, XLIII (1984)}, II:949--964, 1986.

\bibitem{Ga94b}
G.~Gallavotti.
\newblock Twistless kam tori.
\newblock {\em Communications in Mathematical Physics}, 164:145--156, 1994.

\bibitem{El96}
L.~H. Eliasson.
\newblock Absolutely convergent series expansions for quasi--periodic motions.
\newblock {\em Mathematical Physics Electronic Journal (MPEJ)}, 2:33 pages,
  1996.

\bibitem{Ga95d}
G.~Gallavotti.
\newblock Invariant tori: a field theoretic point of view on eliasson's work.
\newblock {\em Advances in Dynamical Systems and Quantum Physics, {\rm Ed. R.
  Figari, World Scientific}}, 164:117--132, 1995.

\bibitem{GBG04}
G.~Gallavotti, F.~Bonetto, and G.~Gentile.
\newblock {\em Aspects of the ergodic, qualitative and statistical theory of
  motion}.
\newblock Springer Verlag, Berlin, 2004.

\bibitem{He69}
K.~Hepp.
\newblock {\em Th\'eorie de la r\'enormalization}, volume~2.
\newblock Springer Verlag, Lecture notes in Physics, 1969.

\bibitem{BG95}
G.~Gallavotti G.~Benfatto.
\newblock {\em Renormalization group}.
\newblock Princeton University Press, Princeton, 1995.

\bibitem{GG05}
G.~Gallavotti and G.~Gentile.
\newblock Degenerate elliptic resonances.
\newblock {\em Communications in Mathematical Physics}, 257:319--362, 2005.

\bibitem{LC}
T.~Levi-Civita.
\newblock {\em Opere Matematiche}, volume~2.
\newblock Accademia Nazionale dei Lincei, Zani\-chelli,, Bologna, 1956.

\end{thebibliography}