Jaroslaw Kwapisz 1998 Nonlinearity 11 547 doi:10.1088/0951-7715/11/3/008
Jaroslaw Kwapisz
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We investigate a model of a charged particle in a uniform magnetic field with resonant nonlinear forcing. The resonance is chosen so that the problem is invariant under a rank 2 lattice of translations in velocities and thus reduces to iteration of a torus map. The rotation set of this map, at least for well-pronounced nonlinearities, has a positive (and easy to estimate) area. This is an indication of `toroidal chaos', and physically corresponds to stochastical heating of the plasma. Our main result is the monotonicity of the rotation set as a function of the amplitude of the wave in the case when the forcing is `saw-tooth-like'.
05.45.Ac Low-dimensional chaos
62M02 Markov processes: hypothesis testing
34C15 Nonlinear oscillations, coupled oscillators
Issue 3 (May 1998)
Received 27 August 1997, in final form 31 December 1997
Jaroslaw Kwapisz 1998 Nonlinearity 11 547
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