We consider the problem of cotangent bundle reduction for non free group actions at zero momentum. We show that in this context the sym-plectic stratification obtained by Sjamaar and Lerman in  refines in two ways: (i) each symplectic stratum admits a stratification which we call the secondary stratification with two distinct types of pieces, one of… (More)
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)
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)
We develop a theory of gauge and dynamical equivalence for Lagrangian systems on Lie algebroids, also studying its relationship with Nöther and non-Nöther conserved quantities.