Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1888)
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Table of contents (9 chapters)
Keywords
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)
Authors and Affiliations
Bibliographic Information
Book Title: Transseries and Real Differential Algebra
Authors: Joris Hoeven
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/3-540-35590-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Softcover ISBN: 978-3-540-35590-8Published: 15 September 2006
eBook ISBN: 978-3-540-35591-5Published: 31 October 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 260
Number of Illustrations: 8 b/w illustrations
Topics: Algebraic Geometry, Difference and Functional Equations, Dynamical Systems and Ergodic Theory