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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)
For the cotangent bundle of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we construct a Witt-Artin decomposition at any point. We also obtain a splitting of the symplectic normal space which is related to the original bundle structure. This splitting is computed only in terms of the group… (More)
For the cotangent bundle T * Q of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal space at any point. We show that this space splits as the direct sum of the cotangent bundle of a linear space and a symplectic linear space coming from reduction of a… (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.