Scaling law in the Standard Map critical function. Interpolating hamiltonian and frequency map analysis

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 $1/q$.