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

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

2003-05-15

arxiv.org/abs/math/0305220v1

Mathematics

Dynamical Systems

26 pages, 3 figures, 13 tables

Scientific paper

10.1088/0951-7715/17/2/017

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.

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