Smooth singular solutions of hyperplane fields. II
A. S. De Medeiros (1992)
Annales scientifiques de l'École Normale Supérieure
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Displaying similar documents to “Smooth singular solutions of hyperplane fields. I”
Smooth singular solutions of hyperplane fields. II
A KAM phenomenon for singular holomorphic vector fields
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Let X be a germ of holomorphic vector field at the origin of and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system. The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets in a neighborhood of the origin. These are...
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We study the existence of global canard surfaces for a wide class of real singular perturbation problems. These surfaces define families of solutions which remain near the slow curve as the singular parameter goes to zero.