From the 2 of 5 linked papers with an AI index.
5 papers
Algebraic independence of solutions to multiple Lotka-Volterra systems
Yutong Duan, Christine Eagles, Léo Jimenez
Consider some non-zero complex numbers with and the associated classical Lotka-Volterra systems \[ \begin{cases} x' = a_i xy + b_i x \newline…
Internality of autonomous algebraic differential equations
Christine Eagles, Léo Jimenez
The paper investigates when solutions of autonomous algebraic ordinary differential equations can be written as rational functions of finitely many fixed solutions (and their deriv…
Domination, fibrations and splitting
Christine Eagles, Léo Jimenez
This article is concerned with finite rank stability theory, and more precisely two classical ways to decompose a type using minimal types. The first is its domination equivalence…
Splitting differential equations using Galois theory
Christine Eagles, Léo Jimenez
This article is interested in pullbacks under the logarithmic derivative of algebraic ordinary differential equations. In particular, assuming the solution set of an equation is in…
Note on a differential algebra bound
Léo Jimenez
In a recent article, Freitag, Moosa and the author showed that in differentially closed fields of characteristic zero, if two types are nonorthogonal, then their n+3 and m+3 Morley…