Jean-Philippe Rolin

Transition maps at non-resonant hyperbolic singularities are o-minimal

Abstract We construct a model complete and o-minimal expansion of the field of real numbers such that, for any planar analytic vector field ξ and any isolated, non-resonant hyperbolic singularity p of ξ, a transition map for ξ at p is definable in . This expansion also defines all convergent generalized power series with natural support and is polynomially bounded.

Quantifier elimination and rectilinearization theorem for generalized quasianalytic algebras

An algebra of germs of real functions is generalised quasianalytic if to each element of the algebra we can associate, injectively, a power series with nonnegative real exponents. We prove a quantifier elimination and a rectilinearisation result for generalised quasianalytic algebras.

Construction of O-minimal Structures from Quasianalytic Classes

I present the method of constructing o-minimal structures based on local reduction of singularities for quasianalytic classes.

Lecture notes on O-minimal structures and real analytic geometry

Preface.- Blowings-up of Vector Fields (F. Cano).- Basics of o-Minimality and Hardy Fields (C. Miller).- Construction of o-Minimal Structures from Quasianalytic Classes (J.-P. Rolin).- Course on Non-Oscillatory Trajectories.- F.S. Sanchez).- Pfaffian Sets and o-Minimality (P. Speissegger).- Theorems of the Complement (A. Fornasiero, T. Servi).

Théorème de Gabrielov et fonctions log-exp-algébriques

Resume Nous obtenons le theoreme de Wilkie sur les fonctions log-exp-algebriques du theoreme du complementaire ≪ explicite ≫ de Gabrielov, et de notre presentation geometrique du theoreme de van den Dries, Macintyre et Marker sur les fonctions log-exp-analytiques.