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Lecture Notes in Mathematics
cover

Transseries and Real Differential Algebra

Authors: van der Hoeven, Joris

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About this book

Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.

Reviews

From the reviews:

"A transseries can be described … as a formal object constructed from the real numbers and an infinitely large variable x using infinite summation, exponentiation, and logarithm. … The author intends the book for non-specialists, including graduate students, and to that end has made the volume self-contained and included exercises. The book is intended for mathematicians working in analysis, model theory, or computer algebra. Algebraists should also find interest in the algebraic properties of the field of transseries." (Andy R. Magid, Zentralblatt MATH, Vol. 1128 (6), 2008)


Table of contents (9 chapters)

Table of contents (9 chapters)
  • Orderings

    Pages 11-32

  • Grid-based series

    Pages 33-55

  • The Newton polygon method

    Pages 57-77

  • Transseries

    Pages 79-96

  • Operations on transseries

    Pages 97-113

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-540-35591-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Transseries and Real Differential Algebra
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1888
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-35591-5
DOI
10.1007/3-540-35590-1
Softcover ISBN
978-3-540-35590-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 260
Number of Illustrations
8 b/w illustrations
Topics