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Variational Problems with Symmetries: A Pfaffian System Approach

Research paper by Paola Morando, Serena Sammarco

Indexed on: 05 May '12Published on: 05 May '12Published in: Acta Applicandae Mathematicae



Abstract

Reduction methods for completely integrable Pfaffian Systems with symmetry are applied to variational problems, providing analogues of the Arnold–Liouville Theorem and Marsden–Weinstein reduction in the Lagrangian setting. A generalization of the Mishchenko–Fomenko Theorem for non Abelian integrability is given in terms of solvable structures.