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Monotonicity of rotation set for toroidal chaos of a resonantly kicked linear oscillator

Jaroslaw Kwapisz

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Recommended by Y Kuramoto

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'.


PACS

05.45.Ac Low-dimensional chaos

05.45.Xt Synchronization; coupled oscillators

02.50.Ey Stochastic processes

02.50.Ga Markov processes

MSC

62M02 Markov processes: hypothesis testing

34C15 Nonlinear oscillations, coupled oscillators

37D45 Strange attractors, chaotic dynamics

60Gxx Stochastic processes

Subjects

Computational physics

Statistical physics and nonlinear systems

Dates

Issue 3 (May 1998)

Received 27 August 1997, in final form 31 December 1997



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