Transseries and Real Differential Algebra

  • Joris van der Hoeven

Part of the Lecture Notes in Mathematics book series (LNM, volume 1888)

Table of contents

  1. Front Matter
    Pages I-XXII
  2. Pages 11-32
  3. Pages 33-55
  4. Pages 79-96
  5. Pages 115-133
  6. Back Matter
    Pages 235-259

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.


Finite Transseries algebra asymptotics differential algebra equation mathematics o-minimality proof surreal numbers theorem variable

Authors and affiliations

  • Joris van der Hoeven
    • 1
  1. 1.Département de Mathématiques, CNRSUniversité Paris-SudOrsay CXFrance

Bibliographic information