Many-Dimensional Poincar\'e Construction and Singularities of Lifted Fields For Implicit Differential Equations

A. O. Remizov

Contemporary Mathematics. Fundamental Directions, Optimal control, Tome 19 (2006), pp. 131-170.

Résumé

The paper is devoted to singular points of the so-called lifted vector fields, which arise in studying systems of implicit differential equations by using the method of lifting the equation to a surface, a generalization of the construction used by Poincaré for a single implicit equation. The author study the phase portraits and renormal forms of such fields in a neighborhood of their singular points. In conclusion, the paper considers the lifted vectors fields generated by Euler–Lagrange and Euler–Poisson equations and fast-slow systems.

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