Thierry Combot

activity

20112025

most citedA note on algebraic potentials and Morales-Ramis theory

27 citations · 62 across the 20 of their papers we have counts for

collaborators

23 papers

math-ph2025

Non-integrability of the $n$ -body problem

Andrzej J. Maciejewski, Maria Przybylska, Thierry Combot

We prove that the classical planar $n$ -body problem when restricted to a common level of the energy and the angular momentum is not integrable except in the case when both values o…

math.CA2024

Liouvillian Solutions of Third Order Differential Equations

Camilo Sanabria, Thierry Combot

Consider a third order linear differential equation $L (f) = 0$ , where $L \in Q (z) [\partial_{z}]$ . We design an algorithm computing the Liouvillian solutions of $L (f) = 0$ . The red…

math.DG2023

Symbolic integration on planar differential foliations

Thierry Combot

We consider the problem of symbolic integration of $\int G (x, y (x)) d x$ where $G$ is rational and $y (x)$ is a non algebraic solution of a differential equation $y^{'} (x) = F (x, y (x))$ wit…

math.AG2023

Hyperelliptic Integrals to Elliptic Integrals

Thierry Combot

Consider a hyperelliptic integral $I = \int P / (Q S) d x$ , $P, Q, S \in K [x]$ , with $[K : Q] < \infty$ . When $S$ is of degree $\leq 4$ , such integral can be ca…

math.DS2022★ 1 cited

Hyperexponential solutions of elliptic difference equations

Thierry Combot

Consider an elliptic curve $C$ with coefficients in $K$ with $[K : Q] < \infty$ and $δ \in C (K)$ a non torsion point. We consider…

math.DS2021

Reduction of symbolic first integrals of planar vector fields

Thierry Combot

Consider a planar polynomial vector field $X$ , and assume it admits a symbolic first integral $F$ , i.e. of the $4$ classes, in growing complexity: Rational, Darbouxian, L…

Non-integrability of the n-body problem

Liouvillian Solutions of Third Order Differential Equations

Symbolic integration on planar differential foliations

Hyperelliptic Integrals to Elliptic Integrals

Hyperexponential solutions of elliptic difference equations

Reduction of symbolic first integrals of planar vector fields

Non-integrability of the $n$ -body problem