Transseries and Real Differential Algebra / by Joris van der Hoeven.

Format:

Book

Author/Creator:

Hoeven, J. van der (Joris), author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1888.

Lecture Notes in Mathematics, 0075-8434 ; 1888

Language:

English

Subjects (All):

Geometry, Algebraic.

Functional equations.

Differentiable dynamical systems.

Algebraic Geometry.

Difference and Functional Equations.

Dynamical Systems and Ergodic Theory.

Local Subjects:

Algebraic Geometry.

Difference and Functional Equations.

Dynamical Systems and Ergodic Theory.

Physical Description:

1 online resource (XII, 260 pages 8 illustrations).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

9783540355915

Access Restriction:

Restricted for use by site license.