title: Biased diffusion inside regular islands under random symplectic perturbations.
abstract: We study the random concatenation of slightly different two-dimensional Hamiltonian maps with a mixed phase space. We consider a regular island whose fixed point is identical for all maps. Trajectories of the concatenated maps near this fixed point are no longer confined to invariant tori. We derive a stochastic model for the distance from the fixed point, which turns out to be a biased random walk with multiplicative noise. We give an analytical prediction of the survival probability of trajectories inside the regular island, which asymptotically is the product of a power law and an exponential. We confirm these results numerically for the parametrically perturbed standard map.
authors.affiliation: Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzerstrasse 38, 01187 Dresden, Germany.
authors.forename: Alexandra
authors.initials: A
authors.lastname: Kruscha
authors.forename: Roland
authors.initials: R
authors.lastname: Ketzmerick
authors.forename: Holger
authors.initials: H
authors.lastname: Kantz
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*