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SINGULAR COTANGENT MODEL

Part of: Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Symplectic geometry, contact geometry Local and nonlocal bifurcation theory

Published online by Cambridge University Press:  18 December 2014

CARLOS CURRÁS-BOSCH
CARLOS CURRÁS-BOSCH*
Affiliation:
Departament d'Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain e-mail: [email protected]
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Abstract

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Any singular level of a completely integrable system (c.i.s.) with non-degenerate singularities has a singular affine structure. We shall show how to construct a simple c.i.s. around the level, having the above affine structure. The cotangent bundle of the desingularized level is used to perform the construction, and the c.i.s. obtained looks like the simplest one associated to the affine structure. This method of construction is used to provide several examples of c.i.s. with different kinds of non-degenerate singularities.

MSC classification

Primary: 53D05: Symplectic manifolds, general
Secondary: 37J35: Completely integrable systems, topological structure of phase space, integration methods 37G05: Normal forms
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 2 , May 2015 , pp. 415 - 430
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

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