Transseries and Real Differential Algebra

1. Auflage 2006
ISBN: 978-3-540-35590-8
Verlag: Springer

Buch, Englisch, Band 1888, 260 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 860 g

Reihe: 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.

Zielgruppe

Research

Autoren/Hrsg.

van der Hoeven, Joris

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.