FM 2003-04 (mp_arc 03-212, arXiv math.DS/0305220)

Author: Alberto Berretti and Guido Gentile

Title: Scaling of the Critical Function for the Standard Map: Some Numerical Results

Abstract: The behavior of the critical function for the breakdown of the homotopically non-trivial invariant (KAM) curves for the standard map, as the rotation number tends to a rational number, is investigated using a version of Greene's residue criterion. The results are compared to the analogous ones for the radius of convergence of the Lindstedt series, in which case rigorous theorems have been proved. The conjectured interpolation of the critical function in terms of the Bryuno function is discussed.

Keywords: Standard map, critical function, KAM theory, Greene's method, Bryuno function

Alberto Berretti
Dipartimento di Matematica
II Universita` di Roma (Tor Vergata)
Via della Ricerca Scientifica, 00133 Roma, Italy
e-mail: berretti@mat.uniroma2.it

Guido Gentile
Dipartimento di Matematica
Universita` di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy
e-mail: gentile@mat.uniroma3.it