title: Trapping scaling for bifurcations in the Vlasov systems.
abstract: We study nonoscillating bifurcations of nonhomogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. Through an unstable manifold expansion, we show that in one spatial dimension the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude-generalizing the "trapping scaling" of plasma physics-or may grow to produce a large-scale modification of the system. Furthermore, resonances are strongly suppressed, leading to different phenomena with respect to the homogeneous case. These analytical findings are illustrated and extended by direct numerical simulations with a cosine interaction potential.
authors.affiliation: Laboratoire J.-A. Dieudonné, Université de Nice-Sophia Antipolis, UMR CNRS 7351, Parc Valrose 06108 Nice Cedex 02, France and Institut Universitaire de France, 75005 Paris, France.
authors.forename: J
authors.initials: J
authors.lastname: Barré
authors.affiliation: Laboratoire J.-A. Dieudonné, Université de Nice-Sophia Antipolis, UMR CNRS 7351, Parc Valrose 06108 Nice Cedex 02, France.
authors.forename: D
authors.initials: D
authors.lastname: Métivier
authors.affiliation: Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
authors.forename: Y Y
authors.initials: YY
authors.lastname: Yamaguchi