Manouchehri, M. Normal forms of implicit differential equations and of Liouville fields. (Formes normales d’équations differéntielles implicites et de champs de Liouville.) (French) Zbl 0854.35021 Ergodic Theory Dyn. Syst. 16, No. 4, 779-789 (1996). Summary: Consider the partial differential equation \(f(x, y(x), dy(x))= 0\), where \(f\) is a smooth real function on \(\mathbb{R}^n\times \mathbb{R}\times (\mathbb{R}^n)^*\). Near each singularity of the characteristic foliation, a Liouville field is associated to the equation; we classify hyperbolic germs of Liouville fields up to symplectic transformations, hence we deduce normal forms for partial differential equations up to transformations which preserve the standard contact form of \(\mathbb{R}^{2n+ 1}\). For \(n= 1\), a theorem of Davydov enables us to deduce normal forms for such equations up to transformations of the \(x\), \(y\) plane. Cited in 1 ReviewCited in 1 Document MSC: 35F20 Nonlinear first-order PDEs 35A22 Transform methods (e.g., integral transforms) applied to PDEs Keywords:Liouville field; hyperbolic germs; normal forms for partial differential equations PDFBibTeX XMLCite \textit{M. Manouchehri}, Ergodic Theory Dyn. Syst. 16, No. 4, 779--789 (1996; Zbl 0854.35021) Full Text: DOI References: [1] Takens, Publications mathématiques I.H.E.S 43 pp 47– (1974) [2] DOI: 10.2307/2372774 · Zbl 0083.31406 · doi:10.2307/2372774 [3] Chaperon, Astérisque 107?108 pp 259– (1983) [4] Chaperon, Astérisque 138?139 pp none– (1986) [5] DOI: 10.1007/BF01078387 · Zbl 0582.34056 · doi:10.1007/BF01078387 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.