title: Double autoresonance in two-dimensional dynamical systems.
abstract: The phenomenon of double autoresonance in dynamical systems with two degrees of freedom is examined. We analyze the motion of a particle in a two-dimensional centrally symmetric potential, subject to a homogeneous quasiperiodic external field of elliptical polarization. It is shown that if the particle has a sufficiently small initial energy, a double resonance is established when the slowly varying driving frequency approaches the linear resonance frequency. As the driving frequency is changed further, the double resonance is maintained, causing a continuous excitation of the oscillator. When nonlinearity becomes significant, the motion transforms into nearly circular oscillations. The necessary conditions for the persistence of the autoresonance are studied in detail.
authors.affiliation: Racah Institute of Physics, Hebrew University of Jerusalem, 91904 Jerusalem, Israel.
authors.forename: U
authors.initials: U
authors.lastname: Rokni
authors.forename: L
authors.initials: L
authors.lastname: Friedland