Bifurcation of relative equilibria in mechanical systems with symmetry

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The relative equilibria of a symmetric Hamiltonian dynamical system are the critical points of the so-called augmented Hamiltonian. The underlying geometric structure of the system is used to decompose the critical point equations and construct a collection of implicitly defined functions and reduced equations describing the set of relative equilibria in a neighborhood of a given relative equilibrium. The structure of the reduced equations is studied in a few relevant situations. In particular, a persistence result of Lerman and Singer [LS98] is generalized to the framework of Abelian proper actions. Also, a Hamiltonian version of the Equivariant Branching Lemma and a study of bifurcations with maximal isotropy are presented. An elementary example is presented to illustrate the use of this approach.
32 pages

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Differential Geometry, Dynamical Systems, Symplectic Geometry, 37G40; 37J15; 37K50; 70H33; 70K50

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http://salesiana.dossiersoluciones.com/handle/123456789/79697

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9912232
 http://arxiv.org/abs/math/9912232

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arXiv