MPEJ Volume 5, No.4, 8pp
Received: Jul 7, 1999, Accepted: Sep 29, 1999

Federico Bonetto, Guido Gentile
On a conjecture for the critical behaviour of KAM tori

ABSTRACT:  At the light of recent results in literature we review a
conjecture formulated in Math. Phys. Electron. J. 1 (1995), paper 5, 1-13,
about the mechanism of breakdown of invariant sets in KAM problems
and the identification of the dominant terms in the perturbative expansion
of the conjugating function. We show that some arguments developed therein
can be carried out further only in some particular directions, so limiting
a possible future research program, and that the mechanism of break down
of invariant tori has to be more complicated than as conjectured
in the quoted paper.