Bifurcation of relative equilibria in mechanical systems with symmetry

摘要: The relative equilibria of a symmetric Hamiltonian dynamical system are the critical points so-called augmented Hamiltonian. underlying geometric structure is used to decompose point equations and construct collection implicitly defined functions reduced describing set in neighborhood given equilibrium. studied few relevant situations. In particular, persistence result Lerman Singer [Nonlinearity 11 (1998) 1637-1649] generalized framework Abelian proper actions. Also, version Equivariant Branching Lemma study bifurcations with maximal isotropy presented. An elementary example illustrates use this approach.