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A topological property of integrable systems


Author: J. C. Álvarez Paiva
Journal: Proc. Amer. Math. Soc. 128 (2000), 2507-2508
MSC (2000): Primary 37J35
DOI: https://doi.org/10.1090/S0002-9939-00-05783-X
Published electronically: April 7, 2000
MathSciNet review: 1756086
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Abstract | References | Similar Articles | Additional Information

Abstract:

If we are given $n$ real-valued smooth functions on $\mathbb{R}^{2n}$ which are in involution, then, under some mild hypotheses, the subset of $\mathbb{R}^{2n}$ where these functions are linearly independent is not simply connected.


References [Enhancements On Off] (What's this?)

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Additional Information

J. C. Álvarez Paiva
Affiliation: Université Catholique de Louvain, Institut de Mathématique Pure et Appl., Chemin du Cyclotron 2, B–1348 Louvain–la–Neuve, Belgium
Email: alvarez@agel.ucl.ac.be

DOI: https://doi.org/10.1090/S0002-9939-00-05783-X
Keywords: Integrable systems, Maslov index, Lagrangian submanifold
Received by editor(s): September 24, 1998
Published electronically: April 7, 2000
Communicated by: Christopher Croke
Article copyright: © Copyright 2000 American Mathematical Society