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Kinetic theory of stellar systems, two-dimensional vortices and HMF model. (English) Zbl 1195.85007

Summary: We discuss the kinetic theories of stellar systems, two-dimensional vortices and Hamiltonian mean field model, stressing their analogies and differences. We describe the evolution of the system as a whole and discuss the timescale of relaxation towards the Boltzmann distribution predicted by statistical mechanics. We also consider the relaxation of a “test” particle in a bath of “field” particles and analyze it with the aid of a Fokker-Planck equation involving a term of diffusion counterbalanced by a friction or a drift.

MSC:

85A05 Galactic and stellar dynamics
70H05 Hamilton’s equations
76B47 Vortex flows for incompressible inviscid fluids
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
85A15 Galactic and stellar structure
83C10 Equations of motion in general relativity and gravitational theory
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