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arXiv · 1909.11344

Towards a classification of bifurcations in Vlasov equations

Julien Barré·David Métivier·Yoshiyuki Y. Yamaguchi
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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 the Casimirs, which are constants of motion, to form a size 3 Jordan block. We derive a three-dimensional reduced noncanonical Hamiltonian system describing this bifurcation: coupling with the Casimirs controls the phase space portrait. 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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Julien Barré, David Métivier, Yoshiyuki Y. Yamaguchi. 2020-01-14. Towards a classification of bifurcations in Vlasov equations. https://doi.org/10.1103/physreve.102.052208

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