Below is the ascii version of the abstract for 13-85. The html version should be ready soon.

Guido Gentile
Invariant curves for exact symplectic twist maps of the cylinder with Bryuno rotation numbers
(466K, pdf)

ABSTRACT.  Since Moser's seminal work it is well known that the invariant curves of smooth 
nearly integrable twist maps of the cylinder with Diophantine rotation number 
are preserved under perturbation. In this paper we show that, in the analytic class, 
the result extends to Bryuno rotation numbers. First, we will show that 
the series expansion for the invariant curves in powers of 
the perturbation parameter can be formally defined, then we shall prove 
that the series converges absolutely in a neighbourhood of the origin. 
This will be achieved using multiscale analysis and renormalisation group techniques 
to express the coefficients of the series as sums of values which are represented 
graphically as tree diagrams and then exploit cancellations 
between terms contributing to the same perturbation order. 
As a byproduct we shall see that, when perturbing linear maps, the series expansion 
for an analytic invariant curve converges for all perturbations 
if and only if the corresponding rotation number satisfies the Bryuno condition.