Overview

"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."

Full Product Details

Author:   Joris van der Hoeven
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2006 ed.
Volume:   1888
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   0.860kg
ISBN:  

9783540355908

ISBN 10:   3540355901
Pages:   260
Publication Date:   15 September 2006
Audience:   College/higher education ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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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.

Reviews

From the reviews: <p> A transseries can be described a ] as a formal object constructed from the real numbers and an infinitely large variable x using infinite summation, exponentiation, and logarithm. a ] 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)

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)

"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)"

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)

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)

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