Lecture Notes on O-Minimal Structures and Real Analytic Geometry

  • Chris Miller
  • Jean-Philippe Rolin
  • Patrick Speissegger

Part of the Fields Institute Communications book series (FIC, volume 62)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Felipe Cano
    Pages 1-41
  3. Chris Miller
    Pages 43-69
  4. Fernando Sanz Sánchez
    Pages 111-177
  5. Patrick Speissegger
    Pages 179-218
  6. Antongiulio Fornasiero, Tamara Servi
    Pages 219-242

About this book

Introduction

​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. ​

Keywords

Hardy fields Pfaffian sets o-Minimal structures quasianalytic classes real analytic geometry vector fields

Editors and affiliations

  • Chris Miller
    • 1
  • Jean-Philippe Rolin
    • 2
  • Patrick Speissegger
    • 3
  1. 1., Department of MathematicsThe Ohio State UniversityColumbusUSA
  2. 2., Institut de mathématiques de BourgogneUniversité de BourgogneDijonFrance
  3. 3., Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-4042-0
  • Copyright Information Springer Science+Business Media New York 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-4041-3
  • Online ISBN 978-1-4614-4042-0
  • Series Print ISSN 1069-5265
  • Series Online ISSN 2194-1564
  • About this book