Transseries and real differential algebra
Author(s)
Bibliographic Information
Transseries and real differential algebra
（Lecture notes in mathematics, 1888）
Springer, c2006
Available at / 63 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||188806045173
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Note
Includes bibliographical references (p. [235]-239) and index
http://dx.doi.org/10.1007/3-540-35590-1
Description and Table of Contents
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 Ecalle'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.
Table of Contents
Orderings.- Grid-based series.- The Newton polygon method.- Transseries.- Operations on transseries.- Grid-based operators.- Linear differential equations.- Algebraic differential equations.- The intermediate value theorem.
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