A method for testing Gµ-stability of relative equilibria in Hamil-tonian systems of the form " kinetic + potential energy " is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group actions and singular momentum values. A normal form for the symplectic matrix at a relative equilibrium is also obtained.
We apply geometric techniques to obtain the necessary and sufficient conditions on the existence and nonlinear stability of self-gravitating Rie-mann ellipsoids having at least two equal axes.
We obtain a theory of stratified Sternberg spaces thereby extending the theory of cotangent bundle reduction for free actions to the singular case where the action on the base manifold consists of only one orbit type. We find that the symplectic reduced spaces are stratified topological fiber bundles over the cotangent bundle of the orbit space. We also… (More)
This paper studies singular contact reduction for cosphere bundles at the zero value of the momentum map. A stratification of the singular quotient, finer than the contact one and better adapted to the bundle structure of the problem, is obtained. The strata of this new stratification are a collection of cosphere bundles and coisotropic or Legendrian… (More)
We obtain an algorithmic construction of the isotropy lattice for a lifted action of a Lie group G on T M and T * M based only on the knowledge of G and its action on M. Some applications to symplectic geometry are also shown.
We present a framework for the study of the local qualitative dynamics of equivariant Hamiltonian flows specially designed for points in phase space with nontrivial isotropy. This is based on the classical construction of structure-preserving tubular neighborhoods for Hamiltonian Lie group actions on symplectic manifolds. This framework is applied to… (More)