Transseries and Real Differential Algebra: 1888 - Brossura

Van Der Hoeven, Joris

 
9783540355908: Transseries and Real Differential Algebra: 1888
Brossura
ISBN 10: 3540355901 ISBN 13: 9783540355908
Casa editrice: Springer Berlin Heidelberg, 2010

Sinossi

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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Recensione

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)

Contenuti

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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Editore
Springer Berlin Heidelberg
Data di pubblicazione
2010
Lingua
Inglese
ISBN 10 
3540355901
ISBN 13 
9783540355908
Rilegatura
Copertina flessibile
Numero di pagine
272
Contatto del produttore
non disponibile
Persona responsabile
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Germania

Altre edizioni note dello stesso titolo

9783540825890: Transseries and Real Differential Algebra

Edizione in evidenza

ISBN 10:  3540825894 ISBN 13:  9783540825890
Casa editrice: Springer, 2008
Brossura