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Transseries and Real Differential Algebra
Paperback
Series: Lecture Notes in Mathematics, Book 1888
ISBN13: 9783540355908
Publisher: Springer
Published: Sep 15 2006
Pages: 260
Weight: 0.90
Height: 0.63 Width: 6.32 Depth: 9.29
Language: English
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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