Bifurcation of relative equilibria in mechanical systems with symmetry

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dc.creatorChossat, Pascal
dc.creatorLewis, Debra
dc.creatorOrtega, Juan-Pablo
dc.creatorRatiu, Tudor S.
dc.date1999-12-30
dc.date.accessioned2026-07-07T05:32:33Z
dc.date.available2026-07-07T05:32:33Z
dc.descriptionThe 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.
dc.description32 pages
dc.identifierhttps://arxiv.org/abs/math/9912232
dc.identifierhttp://arxiv.org/abs/math/9912232
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79697
dc.subjectDifferential Geometry
dc.subjectDynamical Systems
dc.subjectSymplectic Geometry
dc.subject37G40; 37J15; 37K50; 70H33; 70K50
dc.titleBifurcation of relative equilibria in mechanical systems with symmetry
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