A Bazzani et al 1997 J. Phys. A: Math. Gen. 30 27 doi:10.1088/0305-4470/30/1/004
Action diffusion for symplectic maps with a noisy linear frequency
A Bazzani
,
, S Siboni,§ and G Turchetti,§
We consider an area preserving map in the neighbourhood of an elliptic fixed point, whose linear frequency is stochastically perturbed. The nonlinearity couples the random motion in the phase with the action which exhibits a diffusive behaviour. If the unperturbed dynamics is almost integrable and no macroscopic resonant structures are present in the phase space, a Fokker - Planck equation for the action diffusion is derived and its solution shows an excellent agreement with the simulation of the process. The key points are the description of the unperturbed motion by using the normal forms and the derivation of a stochastically perturbed interpolating Hamiltonian for which the action diffusion coefficient is analytically computed. The angle averaging is justified by the much faster time scale on which the angle relaxes to a uniform distribution.
- PACS
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05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
- MSC
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37J35 Completely integrable systems, topological structure of phase space, integration methods
37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) (See also 60H10)
- Subjects
- Dates
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Issue 1 (7 January 1997)
Received 27 November 1995, in final form 17 July 1996
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Action diffusion for symplectic maps with a noisy linear frequency
A Bazzani et al 1997 J. Phys. A: Math. Gen. 30 27
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