title: Flights in a pseudo-chaotic system.
abstract: We consider the problem of transport in a one-parameter family of piecewise rotations of the torus, for rotation number approaching 1∕4. This is a zero-entropy system which in this limit exhibits a divided phase space, with island chains immersed in a "pseudo-chaotic" region. We identify a novel mechanism for long-range transport, namely the adiabatic destruction of accelerator-mode islands. This process originates from the approximate translational invariance of the phase space and leads to long flights of linear motion, for a significant measure of initial conditions. We show that the asymptotic probability distribution of the flight lengths is determined by the geometric properties of a partition of the accelerator-mode island associated with the flight. We establish the existence of flights travelling distances of order O(1) in phase space. We provide evidence for the existence of a scattering process that connects flights travelling in opposite directions.
authors.affiliation: Department of Physics, New York University, 2 Washington Place, New York, New York 10003, USA.
authors.forename: J H
authors.initials: JH
authors.lastname: Lowenstein
authors.forename: F
authors.initials: F
authors.lastname: Vivaldi