On Darboux’s lemma
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- by Hans Samelson PDF
- Proc. Amer. Math. Soc. 70 (1978), 126-128 Request permission
Abstract:
We resurrect Carathéodory’s proof of Darboux’s lemma (normal form $\Sigma d{p_i}d{q_i}$ for a nondegenerate closed 2-form). The proof is simple and straightforward (after eliminating unnecessary steps) and deserves to be better known. It involves, not surprisingly, the canonical differential equations of Hamilton-Jacobi theory.References
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C. Carathéodory, Variationsrechnung und partielle Differentialgleichungen erster Ordnung, Teubner, Leipzig, 1935; English edition: Calculus of variations and partial differential equations of first order, Holden-Day, San Francisco, 1965.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 70 (1978), 126-128
- MSC: Primary 58A10
- DOI: https://doi.org/10.1090/S0002-9939-1978-0474367-0
- MathSciNet review: 0474367