The experimental localization of Aubry-Mather sets using regularization techniques inspired by viscosity theory.
We provide a new method for the localization of Aubry-Mather sets in quasi-integrable two-dimensional twist maps. Inspired by viscosity theories, we introduce regularization techniques based on the new concept of "relative viscosity and friction," which allows one to obtain regularized parametrizations of invariant sets with irrational rotation number. Such regularized parametrizations allow one to compute a curve in the phase-space that passes near the Aubry-Mather set, and an invariant measure whose density allows one to locate the gaps on the curve. We show applications to the "golden" cantorus of the standard map as well as to a more general case.
Guzzo
Massimiliano
M
Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, via Trieste 63, 35121 Padova, Italy.
Bernardi
Olga
O
Cardin
Franco
F