Diffusion limit for a slow-fast standard map
Apparaît dans la collection : Probabilistic limit theorems for dynamical systems / Théorèmes limites probabilistes pour les systèmes dynamiques
Consider the map $(x, z) \mapsto (x + \epsilon^{-\alpha} \sin (2\pi x) + \epsilon^{-(1+\alpha)}z, z + \epsilon \sin(2\pi x))$, which is conjugate to the Chirikov standard map with a large parameter. For suitable $\alpha$, we obtain a central limit theorem for the slow variable $z$ for a (Lebesgue) random initial condition. The result is proved by conjugating to the Chirikov standard map and utilizing the formalism of standard pairs. Our techniques also yield for the Chirikov standard map a related limit theorem and a ''finite-time'' decay of correlations result. This is joint work with Alex Blumenthal and Ke Zhang.
