Patrick Bonckaert

Linearization of germs of hyperbolic vector fields

We develop a normal form to express asymptotically a conjugacy between a germ of resonant vector field and its linear part. We show that such an asymptotic expression can be written in terms of functions of the Logarithmic Mourtada type. To cite this article: P Bonckaert et al., C. R. Acad. Sci. Paris, Ser. I336 (2003)

Local Analytic Models for Families of Hyperbolic Vector Fields

We study local analytic models for hyperbolic singularities of analytic families of real analytic vector fields. We emphasize on those cases where the normal form theorems of Poincaré and Siegel do not apply, for example for a family of saddles. We also consider the preservation of possible symmetries.

Complete lift transformations for second order differential equations

Abstract Canonical forms of second order differential equations of the form x″ = f(x,x′) are investigated with respect to complete lift transformations, This gives normal forms of observed dynamics of such a system and yields moduli of stability for complete lift equivalence.