Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields

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...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Author: Klajbor-Goderich, S.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209443
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields / S. Klajbor-Goderich // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary: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 the 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 the stability of Hamiltonian relative equilibria.
ISSN:1815-0659