Science, Engineering, and Mathematics (SEM) at the Timbuktu Academy

Abstract

We study conjugacy of formal derivations on fields of generalised power series in characteristic 0. Casting the problem of Poincaré resonance in terms of asymptotic differential algebra, we give conditions for conjugacy of parabolic flat log-exp transseries, flat grid-based transseries, logarithmic transseries, power series with exponents and coefficients in an ordered field, and formal Puiseux series.0 ) for all h 2 S with v(h) > 0. Then the derivations f @ and g @ are conjugate over Aut(S), i.e. there is a = exp(h @) 2 Aut(S) such that (g @) inv = f @.