Nonlinear Stability of Relative Equilibria and Isomorphic Vector Fields

Symmetry Integrability and Geometry-Methods and Applications

article

Stefan Klajbor-Goderich¹ 

[1] Department of Mathematics, University of Illinois at Urbana-Champaign

关键词: equivariant dynamics;    relative equilibria;    orbital stability;    Hamiltonian systems;   

DOI  :  10.3842/SIGMA.2018.021

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown