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Publications Influence

Computing necessary integrability conditions for planar parametrized homogeneous potentials

- A. Bostan, Thierry Combot, M. S. E. Din
- Mathematics, Computer Science
- ISSAC
- 21 May 2014

TLDR

3 1- PDF

A Binomial-like Matrix Equation

- A. Bostan, Thierry Combot
- Mathematics, Computer Science
- Am. Math. Mon.
- 1 August 2012

TLDR

3 1

A note on algebraic potentials and Morales–Ramis theory

- Thierry Combot
- Mathematics
- 21 September 2012

We present various properties of algebraic potentials, and then prove that some Morales–Ramis theorems readily apply for such potentials even if they are not in general meromorphic potentials. This… Expand

17 1- PDF

Third order integrability conditions for homogeneous potentials of degree -1

- Thierry Combot, C. Koutschan
- Mathematics, Physics
- 25 November 2011

We prove an integrability criterion of order 3 for a homogeneous potential of degree −1 in the plane. Still, this criterion depends on some integer and it is impossible to apply it directly except… Expand

12- PDF

Symbolic Computations of First Integrals for Polynomial Vector Fields

- Guillaume Chèze, Thierry Combot
- Mathematics, Computer Science
- Found. Comput. Math.
- 23 October 2017

TLDR

2- PDF

Integrability conditions at order 2 for homogeneous potentials of degree -1

- Thierry Combot
- Mathematics, Physics
- 26 September 2011

We prove a meromorphic integrability condition at order 2 near a homothetic orbit for a meromorphic homogeneous potential of degree -1, which extend the Morales Ramis conditions of order 1.… Expand

12- PDF

Meromorphically integrable homogeneous potentials with multiple Darboux points

- Thierry Combot
- Mathematics, Physics
- 28 January 2013

We prove that the only meromorphically integrable planar homogeneous potential of degree k -2,0,2 having a multiple Darboux point is the potential invariant by rotation. This case is a singular case… Expand

1- PDF

Integrability conditions of geodesic flow on homogeneous Monge manifolds

- Thierry Combot, T. Waters
- Mathematics
- Ergodic Theory and Dynamical Systems
- 30 September 2013

Abstract We prove a meromorphic integrability criterion for the geodesic flow of an algebraic manifold of the form ${z}^{p} - f({x}_{1} , \ldots , {x}_{n} )= 0$ with the induced metric of ${… Expand

4

Integrable homogeneous potentials of degree −1 in the plane with small eigenvalues

- Thierry Combot
- Mathematics, Physics
- 27 October 2011

We give a complete classification of meromorphically integrable homogeneous potentials V of degree −1 which are real analytic on R 2 \ {0}. In the more general case when V is only meromorphic on an… Expand

2- PDF

Bi-homogeneity and integrability of rational potentials

- Thierry Combot, A. Maciejewski, M. Przybylska
- Mathematics
- 15 May 2020

Abstract In this paper we consider natural Hamiltonian systems with two degrees of freedom for which Hamiltonian function has the form H = 1 2 ( p 1 2 + p 2 2 ) + V ( q 1 , q 2 ) and potential V ( q… Expand

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