ENGLISH

Transseries and real differential algebra

By Joris van der Hoeven (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2006
ISBN
9783540355908, 9783540355915, 3540355901
DOI
10.1007/3-540-35590-1
Open Library ID
OL9056628M
Language
english
Format
PDF
Filesize
4 MB (4010766 bytes)
Series
Lecture Notes in Mathematics 1888
Edition
1
Pages
260\264
Topic
Mathematics Algebra
Time added
2009-08-06 05:14:26
Algebraic Geometry; Difference and Functional Equa

Description

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.

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