T. Carletti, J. Laskar
Scaling law in the Standard Map critical function. Interpolating hamiltonian
and frequency map analysis.
(393K, AMS-LaTeX 2e with 8 PS Figures")
ABSTRACT. We study the behaviour of the Standard map critical function in a
neighbourhood of a fixed resonance, that is the scaling law at the
fixed resonance.
We prove that for the fundamental resonance the scaling law is
linear. We show numerical evidence that for the other resonances
$p/q$, $q \geq 2$, $p \neq 0$ and $p$ and $q$ relatively prime,
the scaling law follows a power--law with exponent $1/q$.