Formal conjugacy and asymptotic differential algebra
Vincent Bagayoko
TL;DR
This paper investigates the conjugacy of formal derivations in fields of generalized power series, providing conditions for conjugacy across various types of transseries and formal series using asymptotic differential algebra.
Contribution
It introduces new conditions for conjugacy of formal derivations in generalized power series fields, connecting Poincaré resonance with asymptotic differential algebra.
Findings
Conditions for conjugacy of parabolic flat log-exp transseries
Conditions for conjugacy of flat grid-based transseries
Conditions for conjugacy of logarithmic and power series
Abstract
We study conjugacy of formal derivations on fields of generalised power series in characteristic 0. Casting the problem of Poincar\'e 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.
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Taxonomy
TopicsNumerical methods for differential equations · Polynomial and algebraic computation