On a conjecture for the critical behaviour of KAM tori

Details On a conjecture for the critical behaviour of KAM tori On a conjecture for the critical behaviour of KAM tori

1999-07-07

arxiv.org/abs/chao-dyn/9907014v1

Nonlinear Sciences

Chaotic Dynamics

8 pages

Scientific paper

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.

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