Asymptotic Differential Algebra and Model Theory of Transseries
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
Häftad, 2017
782 kr
Transseries and Real Differential Algebra
603 kr
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Beskrivning
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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