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Quasianalytic Denjoy-Carleman classes and o-minimality

- J. Rolin, P. Speissegger, A. Wilkie
- Mathematics
- 21 March 2003

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 closure… Expand

161 10- PDF

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 un… Expand

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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 is… Expand

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Quasi‐analytic solutions of analytic ordinary differential equations and o‐minimal structures

- J. Rolin, F. Sanz, R. Schäfke
- Mathematics
- 1 September 2007

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 true… Expand

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A Note on the Weierstrass Preparation Theorem in Quasianalytic Local Rings

- A. Parusinski, J. Rolin
- Mathematics
- Canadian Mathematical Bulletin
- 18 March 2013

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 Theoremholds… Expand

13 1- PDF

Lecture notes on o-minimal structures and real analytic geometry

- C. Miller, J. Rolin, P. Speissegger
- Mathematics
- 2012

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… Expand

11- PDF

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

- Tobias Kaiser, J. Rolin, P. Speissegger
- Mathematics
- 23 December 2006

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… Expand

31- PDF

[Particular elements of the cardiac rhythm in the Wolff-Parkinson-White syndrome: report of two cases (author's transl)].

- R. Malebranche, C. Ameur-Hedrich, +5 authors G. Laval
- Medicine
- Annales de cardiologie et d'angeiologie
- 1 May 1978

Tubular neighborhoods of orbits of power-logarithmic germs

- P. Mardesi'c, M. Resman, J. Rolin, V. Zupanovic
- Mathematics
- 21 November 2019

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 analytic… Expand

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