By Joris van der Hoeven
Transseries are formal gadgets made out of an infinitely huge variable x and the reals utilizing countless summation, exponentiation and logarithm. they're appropriate for modeling "strongly monotonic" or "tame" asymptotic suggestions to differential equations and locate their foundation in a minimum of 3 various parts of arithmetic: research, version idea and machine algebra. They play a vital position in Écalle's evidence of Dulac's conjecture, that is heavily relating to Hilbert's sixteenth challenge. the purpose of the current e-book is to offer an in depth and self-contained exposition of the idea of transseries, within the desire of creating it extra available to non-specialists.
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