Dynamic and normal forms of implicit differential equations
The author studies the local dynamics of implicit differential equations of the form \(F(x,y,dy)=0\) in a neighbourhood of a singular point. He uses relationships between implicit systems and Liouvillian vector fields. Symplectic classification of the latter implies the classification of implicit equations by contact transformations. The author uses results on normal forms of vector fields of Brjuno, Siegel and Stolovitch in the complex case and of Sternberg in the real one, adapted to Liouvillian vector fields and symplectic transformations. He gives the classification of implicit differential equations according to dynamical invariants and conditions for the existence of local solutions based on normal forms.
scientific article; zbMATH DE number 6387327
scientific article