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شنبه 19 شهریور 1390

Transseries and real differential algebra ebook

نویسنده: Latrell Santos   

Transseries and real differential algebra




Author: Joris Van Der Hoeven
Type: eBook
Date Released: 2006
Format: pdf
Language: English
Page Count: 264
Isbn10 Code: 3540355901
Isbn13 Code: 9783540355908


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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