1999/12/30 by Pascal Chossat, Debra Lewis, Chossat, Pascal +5
Mathematics · #37G40 #37J15 #37K50 #70H33 #70K50 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.DS #math.SG #msc:37G40 #msc:37J15 #msc:37K50 #msc:70H33 #msc:70K50
paper · pdf · doi:10.48550/arxiv.math/9912232
32 pages
arxiv created 1999/12/30 · arxiv updated 2009/11/30
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.