By Joris van der Hoeven
Transseries are formal gadgets created from an infinitely huge variable x and the reals utilizing countless summation, exponentiation and logarithm. they're compatible for modeling "strongly monotonic" or "tame" asymptotic suggestions to differential equations and locate their foundation in no less than 3 assorted components of arithmetic: research, version concept and laptop algebra. They play an important function in Écalle's facts of Dulac's conjecture, that is heavily regarding Hilbert's sixteenth challenge. the purpose of the current publication is to offer a close and self-contained exposition of the idea of transseries, within the desire of creating it extra obtainable to non-specialists.
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