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Quasianalytic Denjoy-Carleman classes and o-minimality
We show that the expansion of the real field generated by the functions of a quasianalytic Denjoy-Carleman class is model complete and o-minimal, provided that the class satisfies certain closureExpand
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An o-minimal structure which does not admit $C^{\infty }$ cellular decomposition
Nous presentons un exemple de structure o-minimale n'admettant pas la propriete de decomposition cellulaire C ∞ . Pour ce faire, nous construisons une fonction H dont le germe en 0 admet unExpand
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Non-oscillating integral curves and valuations
Let X be an analytic vector field on a real analytic m-dimensional manifold M. Consider an integral curve g : t 7! gðtÞ, tf 0, of X having a unique o-limit point p. We assume that g isExpand
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Quasi‐analytic solutions of analytic ordinary differential equations and o‐minimal structures
It is well known that the non-spiraling leaves of real analytic foliations of codimension 1 all belong to the same o-minimal structure. Naturally, the question arises if the same statement is trueExpand
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A Note on the Weierstrass Preparation Theorem in Quasianalytic Local Rings
Abstract Consider quasianalytic local rings of germs of smooth functions closed under composition, implicit equation, and monomial division. We show that if the Weierstrass Preparation TheoremholdsExpand
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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 onExpand
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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 pExpand
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Tubular neighborhoods of orbits of power-logarithmic germs
We consider a class of power-logarithmic germs. We call them parabolic Dulac germs, as they appear as Dulac germs (first-return germs) of hyperbolic polycycles. In view of formal or analyticExpand
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