Format:
Online-Ressource (XII, 260 p, digital)
ISBN:
9783540355915
Series Statement:
Lecture Notes in Mathematics 1888
Content:
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.
Content:
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.
Note:
Dissertation
,
Includes bibliographical references (p. [235]-239) and index
Additional Edition:
ISBN 9783540355908
Additional Edition:
Buchausg. u.d.T. Van der Hoeven, Joris, 1971 - Transseries and real differential algebra Berlin, Heidelberg [u.a.] : Springer, 2006 ISBN 3540355901
Additional Edition:
ISBN 9783540355908
Language:
English
Subjects:
Mathematics
Keywords:
Differentialalgebra
;
Differentialalgebra
DOI:
10.1007/3-540-35590-1
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Author information:
Van der Hoeven, Joris 1971-
Bookmarklink
