Thierry Combot

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20112025

most citedA note on algebraic potentials and Morales-Ramis theory

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

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14 papers · 1 filter

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…

math.DS2018

A symplectic Kovacic's algorithm in dimension 4

Thierry Combot, Camilo Sanabria

Let $L$ be a $4$ th order differential operator with coefficients in $K (z)$ , with $K$ a computable algebraically closed field. The operator $L$ is called symplecti…

math.DS2018★ 2 cited

Non-integrability of the minimum-time Kepler problem

Michael Orieux, Jean-Baptiste Caillau, Jacques Féjoz +1

We prove that the minimum-time controlled Kepler problem is not Liouville integrable in the class of meromorphic functions, via the Moralès-Ramis theory.

math.DS2017

Necessary and sufficient conditions for meromorphic integrability near a curve

Thierry Combot

Let us consider a vector field $X$ meromorphic on a neighbourhood of an algebraic curve $Γ ˉ \subset P^{n}$ such that $Γ$ is a particular solution of $X$ . The vector field…

math.DS2017★ 5 cited

Rational integrability of trigonometric polynomial potentials on the flat torus

Thierry Combot

We consider a lattice $L \subset R^{n}$ and a trigonometric potential $V$ with frequencies $k \in L$ . We then prove a strong integrability condition on $V$ ,…