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＜電子ブック＞
Transseries and Real Differential Algebra / by Joris van der Hoeven
(Lecture Notes in Mathematics. ISSN:16179692 ; 1888)

版	1st ed. 2006.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	XII, 260 p. 8 illus : online resource
著者標目	*van der Hoeven, Joris author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Difference equations LCSH:Functional equations LCSH:Dynamical systems FREE:Algebraic Geometry FREE:Difference and Functional Equations FREE:Dynamical Systems
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/3-540-35590-1

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