Lecture notes on o-minimal structures and real analytic geometry
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Bibliographic Information
Lecture notes on o-minimal structures and real analytic geometry
（Fields Institute communications, v. 62）
Springer , Fields Institute for Research in Mathematical Sciences, c2012
- : softcover
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Note
Includes bibliographical references
Description and Table of Contents
Description
This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses.
This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations.
Table of Contents
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).
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