By Joris van der Hoeven
Transseries are formal gadgets produced from an infinitely huge variable x and the reals utilizing limitless summation, exponentiation and logarithm. they're appropriate for modeling "strongly monotonic" or "tame" asymptotic options to differential equations and locate their foundation in at the very least 3 various parts of arithmetic: research, version concept and computing device algebra. They play an important position in Écalle's facts of Dulac's conjecture, that's heavily concerning Hilbert's sixteenth challenge. the purpose of the current publication is to offer an in depth and self-contained exposition of the idea of transseries, within the wish of constructing it extra obtainable to non-specialists.
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