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Published on: July 19, 2016
Towards a classification of bifurcations in Vlasov equations
J Barré1, D Métivier2, Y Y Yamaguchi3
1Institut Denis Poisson, Université d'Orléans, CNRS, Université de Tours, France and Institut Universitaire de France, Bâtiment de mathématiques, Rue de Chartres, B.P. 6759, 45067, Orléans cedex 2, France.
Abstract:
We propose a classification of bifurcations of Vlasov equations, based on the strength of the resonance between the unstable mode and the continuous spectrum on the imaginary axis. We then identify and characterize a new type of generic bifurcation where this resonance is weak, but the unstable mode couples with a stable mode and a Casimir invariant of the system to form a size-3 Jordan block. We derive a three-dimensional reduced noncanonical Hamiltonian system describing this bifurcation. Comparison of the reduced dynamics with direct numerical simulations on a test case gives excellent agreement. We finally discuss the relevance of this bifurcation to specific physical situations.
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