Fields Institute Communications

Lecture Notes on O-Minimal Structures and Real Analytic Geometry

Editors: Miller, Chris, Rolin, Jean-Philippe, Speissegger, Patrick (Eds.)

  • ​Presents material produced in conjunction with the Thematic Program in O-minimal Structures and Real Analytic Geometry, held at the Fields Institute
  • Collects material that is elsewhere unavailable or spread across many different sources such as research papers, conference proceedings, and PhD theses
  • Reflects original content, such as developments and insights that arose since the original research papers were published​
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About this book

​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 (6 chapters)

  • Blowings-Up of Vector Fields

    Cano, Felipe

    Pages 1-41

  • Basics of O-minimality and Hardy Fields

    Miller, Chris

    Pages 43-69

  • Construction of O-minimal Structures from Quasianalytic Classes

    Rolin, Jean-Philippe

    Pages 71-109

  • Course on Non-oscillatory Trajectories

    Sánchez, Fernando Sanz

    Pages 111-177

  • Pfaffian Sets and O-minimality

    Speissegger, Patrick

    Pages 179-218

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4614-4042-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-1-4614-4041-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-1-4939-0102-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Lecture Notes on O-Minimal Structures and Real Analytic Geometry
Editors
  • Chris Miller
  • Jean-Philippe Rolin
  • Patrick Speissegger
Series Title
Fields Institute Communications
Series Volume
62
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-4042-0
DOI
10.1007/978-1-4614-4042-0
Hardcover ISBN
978-1-4614-4041-3
Softcover ISBN
978-1-4939-0102-9
Series ISSN
1069-5265
Edition Number
1
Number of Pages
VIII, 244
Topics