Transseries and Real Differential Algebra

Joris van der Hoeven

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English

Springer Verlag
01 November 2006

Cybernetics & systems theory; Mathematics & Sciences; Mathematics; Differential calculus & equations; Algebraic geometry

Series: Lecture Notes in Mathematics

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.

By: Joris van der Hoeven
Imprint: Springer Verlag
Country of Publication: Germany
Dimensions: Height: 235mm, Width: 155mm, Spine: 14mm
Weight: 860g
ISBN: 9783540355908
ISBN 10: 3540355901
Series: Lecture Notes in Mathematics
Publication Date: 01 November 2006
Audience: College/higher education , A / AS level
Format: Paperback
Publisher's Status: Active

Reviews for Transseries and Real Differential Algebra

"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)"