Geodesic
Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542–587] in his study of vector fields on differentiable stacks. Here we argue in favor of the usefulness of replacing an equivariant vector field by an isomorphic one to study nonlinear stability of relative equilibria. In particular, we use this idea to obtain a criterion for nonlinear stability. As an application, we offer an alternative proof of Montaldi and Rodríguez-Olmos's criterion [arXiv:1509.04961] for stability of Hamiltonian relative equilibria.
Keywords: equivariant dynamics; relative equilibria; orbital stability; Hamiltonian systems. 
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     author = {Stefan Klajbor-Goderich},
     title = {Nonlinear {Stability} of {Relative} {Equilibria} and {Isomorphic} {Vector} {Fields}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a20/}
}
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Stefan Klajbor-Goderich. Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a20/

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