Zobrazeno 1 - 10
of 76
pro vyhledávání: '"Combot, Thierry"'
Autor:
Sanabria, Camilo, Combot, Thierry
Consider a third order linear differential equation $L(f)=0$, where $L\in\mathbb{Q}(z)[\partial_z]$. We design an algorithm computing the Liouvillian solutions of $L(f)=0$. The reducible cases devolve to the classical case of second order operators,
Externí odkaz:
http://arxiv.org/abs/2402.05143
Autor:
Combot, Thierry
We consider the problem of symbolic integration of $\int G(x,y(x)) dx$ where $G$ is rational and $y(x)$ is a non algebraic solution of a differential equation $y'(x)=F(x,y(x))$ with $F$ rational. As $y$ is transcendental, the Galois action generates
Externí odkaz:
http://arxiv.org/abs/2306.12573
Autor:
Combot, Thierry
Consider a hyperelliptic integral $I=\int P/(Q\sqrt{S}) dx$, $P,Q,S\in\mathbb{K}[x]$, with $[\mathbb{K}:\mathbb{Q}]<\infty$. When $S$ is of degree $\leq 4$, such integral can be calculated in terms of elementary functions and elliptic integrals of th
Externí odkaz:
http://arxiv.org/abs/2303.14013
Autor:
Combot, Thierry
Consider an elliptic curve $\mathcal{C}$ with coefficients in $\mathbb{K}$ with $[\mathbb{K}:\mathbb{Q}]<\infty$ and $\delta \in \mathcal{C}(\mathbb{K})$ a non torsion point. We consider an elliptic difference equation $\sum_{i=0}^l a_i(p) f(p\oplus
Externí odkaz:
http://arxiv.org/abs/2205.00041
Autor:
Combot, Thierry
Consider a planar polynomial vector field $X$, and assume it admits a symbolic first integral $\mathcal{F}$, i.e. of the $4$ classes, in growing complexity: Rational, Darbouxian, Liouvillian and Riccati. If $\mathcal{F}$ is not rational, it is someti
Externí odkaz:
http://arxiv.org/abs/2111.10809
Autor:
Combot, Thierry
Consider a superelliptic integral $I=\int P/(Q S^{1/k}) dx$ with $\mathbb{K}=\mathbb{Q}(\xi)$, $\xi$ a primitive $k$th root of unity, $P,Q,S\in\mathbb{K}[x]$ and $S$ has simple roots and degree coprime with $k$. Note $d$ the maximum of the degree of
Externí odkaz:
http://arxiv.org/abs/2103.04134
Autor:
Combot, Thierry
Let $H$ be a hyperexponential function in $n$ variables $x=(x_1,\dots,x_n)$ with coefficients in a field $\mathbb{K}$, $[\mathbb{K}:\mathbb{Q}] <\infty$, and $\omega$ a rational differential $1$-form. Assume that $H\omega$ is closed and $H$ transcend
Externí odkaz:
http://arxiv.org/abs/1901.09029
Autor:
Combot, Thierry, Sanabria, Camilo
Let $L$ be a $4$th order differential operator with coefficients in $\mathbb{K}(z)$, with $\mathbb{K}$ a computable algebraically closed field. The operator $L$ is called symplectic when up to rational gauge transformation, the fundamental matrix of
Externí odkaz:
http://arxiv.org/abs/1802.01023
We prove that the minimum-time controlled Kepler problem is not Liouville integrable in the class of meromorphic functions, via the Moral\`es-Ramis theory.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/1801.04198
Autor:
Chèze, Guillaume, Combot, Thierry
In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing, if it exists, a rational, Darbouxian, Liouvillian or Ricca
Externí odkaz:
http://arxiv.org/abs/1710.08225