Transseries and Real Differential Algebra

• Main Author: Hoeven, Joris van der (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Lecture Notes in Mathematics, 1888
• Subjects: Mathematics.; Algebraic geometry.; Difference equations.; Functional equations.; Dynamics.; Ergodic theory.; Algebraic Geometry.; Difference and Functional Equations.; Dynamical Systems and Ergodic Theory.
• Physical Description: XII, 260 p. 8 illus. online resource.
• ISBN: 9783540355915
• ISSN: 0075-8434 ;

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.