Local analytic models for families of hyperbolic vector fields

Patrick Bonckaert & Koen Neirynck

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 Poincar\'{e} and Siegel do not apply, for example for a family of saddles. We also consider the preservation of possible symmetries.