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 Ecalle'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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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 Ecalle'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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Imprint | Springer-Verlag |
Country of origin | Germany |
Series | Lecture Notes in Mathematics, 1888 |
Release date | September 2006 |
Availability | Expected to ship within 10 - 15 working days |
First published | 2006 |
Authors | Joris van der Hoeven |
Dimensions | 235 x 155 x 14mm (L x W x T) |
Format | Paperback |
Pages | 260 |
Edition | 2006 ed. |
ISBN-13 | 978-3-540-35590-8 |
Barcode | 9783540355908 |
Categories | |
LSN | 3-540-35590-1 |