Transseries and Real Differential Algebra: 1888 (Lecture Notes in Mathematics, 1888) - Tapa blanda

Van Der Hoeven, Joris

 
9783540355908: Transseries and Real Differential Algebra: 1888 (Lecture Notes in Mathematics, 1888)
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ISBN 10: 3540355901 ISBN 13: 9783540355908
Editorial: Springer Berlin Heidelberg, 2010

Sinopsis

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.

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Críticas

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)

Reseña del editor

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer Berlin Heidelberg
Año de publicación
2010
Idioma
Inglés
ISBN 10 
3540355901
ISBN 13 
9783540355908
Encuadernación
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Número de páginas
272
Contacto del fabricante
no disponible
Persona responsable
CMN Printpool Inh. Mathis Neumann
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Hamburg
Alemania

Otras ediciones populares con el mismo título

9783540825890: Transseries and Real Differential Algebra

Edición Destacada

ISBN 10:  3540825894 ISBN 13:  9783540825890
Editorial: Springer, 2008
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