A topological property of integrable systems
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- by J. C. Álvarez Paiva PDF
- Proc. Amer. Math. Soc. 128 (2000), 2507-2508 Request permission
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
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- P. Erdös and T. Grünwald, On polynomials with only real roots, Ann. of Math. (2) 40 (1939), 537–548. MR 7, DOI 10.2307/1968938
- C. Viterbo, A new obstruction to embedding Lagrangian tori, Invent. Math. 100 (1990), no. 2, 301–320. MR 1047136, DOI 10.1007/BF01231188
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
- Received by editor(s): September 24, 1998
- Published electronically: April 7, 2000
- Communicated by: Christopher Croke
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2507-2508
- MSC (2000): Primary 37J35
- DOI: https://doi.org/10.1090/S0002-9939-00-05783-X
- MathSciNet review: 1756086