Field theory and KAM tori

Details Field theory and KAM tori Field theory and KAM tori

1993-03-20

arxiv.org/abs/chao-dyn/9503006v1

Mathematical Physics Electronic Journal, MPEJ, 1, 1995 (http://www.ma.utexas.edu/mpej)

Nonlinear Sciences

Chaotic Dynamics

11 pages, compile with dvips to get the figure

Scientific paper

The parametric equations of KAM tori for a quasi integrable system, are shown to be one point Schwinger functions of a suitable euclidean quantum field theory on the torus. KAM theorem is equivalent to a ultraviolet stability theorem. A renormalization group treatment of the field theory leads to a resummation of the formal pertubation series and to an expansion in terms of new parameters (identified as a family of renormalization constants). The new parameters are analytic in the coupling (at small coupling): the breakdown of the tori at large coupling is speculated to be related to the crossing of a "critical" surface at a value where the renormalization constants are still finite. A mechanism for the possible universality of the singularities of parametric equations for the invariant tori, in their parameter dependence as well as in the coupling dependence, is proposed.}

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