Preprints

Liouvillian Solutions of Third Order Differential Equations
Camilo Sanabria and Thierry Combot
[arxivpdf]

Symbolic integration on planar differential foliations
Thierry Combot
[arxivpdf]

Reduction of symbolic first integrals of planar vector fields
Thierry Combot
[arxivpdf]

Hyperexponential solutions of elliptic difference equations
Thierry Combot
[arxivpdf]

Necessary and sufficient conditions for meromorphic integrability near a curve
Thierry Combot
[arxivpdf]

Publications

Hyperelliptic Integrals to Elliptic Integrals
Thierry Combot
ISSAC 2023, july 2023 pages 191-198 [link] [arxivpdf]
Non-integrability of a model of elastic dumbbell satellite
Thierry Combot
Nonlinear Dynamics volume 106, pages 125–146 (2021) [link]
Integrability of the generalised Hill problem
Thierry Combot
Nonlinear Dynamics volume 107, pages 1989–2002 (2022) [link]
Elementary Integration of Superelliptic Integrals
Thierry Combot
ISSAC 2021, july 2021 pages 99-106 [link] [arxivpdf]
N-body Dynamics on an Infinite Cylinder: the Topological Signature in the Dynamics
Jaime Andrade, Stefanella Boatto, Thierry Combot, Gladston Duarte & Teresinha J. Stuchi
Regular and Chaotic Dynamics volume 25, pages 78–110(2020) [link]
Bi-homogeneity and integrability of rational potentials
Thierry Combot, Andrzej Maciejewski and Maria Przybylska
Journal of Differential Equations Volume 268, Issue 11, 15 May 2020, Pages 7012-7028 [link]
Symbolic Computations of First Integrals for Polynomial Vector Fields
Guillaume Cheze and Thierry Combot
Foundations of Computational Mathematics volume 20, pages 681–752(2020) [link] [arxivpdf]
Symbolic integration of hyperexponential 1-forms
Thierry Combot
ISSAC 2019, july 2019 pages 98-105 [link] [arxivpdf]
Integrability of the one dimensional Schroedinger equation
Thierry Combot
Journal of Mathematical Physics 59, 022105 (2018) [link] [arxivpdf]
Non-integrability of the minimum-time Kepler problem
Michael Orieux, Jean-Baptiste Caillau, Jacques Féjoz, Thierry Combot
Journal of Geometry and Physics Volume 132, October 2018, Pages 452-459 [link] [arxivpdf]
A symplectic Kovacic's algorithm in dimension 4
Thierry Combot and Camilo Sanabria
ISSAC 2018, july 2018 pages 143-150 [link] [arxivpdf]
Rational integrability of trigonometric polynomial potentials on the flat torus
Thierry Combot
Regular and Chaotic Dynamics (2017) 22: 386. [link] [arxivpdf]
Higher variational equation techniques for the integrability of homogeneous potentials
Thierry Combot
Variational Methods In Imaging and Geometric Control, 18, De Gruyter, pp.365-386, 2017, Radon Series on Computational and Applied Mathematics 9783110430394 [link]
Integrable homogeneous potentials of degree −1 in the plane with small eigenvalues
Thierry Combot
Ann. Inst. Fourier, 66(6) :2253 2298, 2016 [link] [arxivpdf]
Integrability and non integrability of some n body problems
Thierry Combot
Recent Advances in Celestial and Space Mechanics. Mathematics for Industry, vol 23. Springer, Cham 2016 [link] [arxivpdf]
Integrability methods in the time minimal coherence transfer for Ising chains of three spins
Thierry Combot
Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 2015, Special issue on optimal control and related fields, 35 (9), pp.4095-4114. [link] [halpdf]
Computing necessary integrability conditions for planar parametrized homogeneous potentials
Alin Bostan, Thierry Combot, Safey El Din Mohab
ISSAC '14 Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation pages 67-74 [link] [arxivpdf]
A note on algebraic potentials and Morales-Ramis theory
Thierry Combot
Celestial Mechanics and Dynamical Astronomy, April 2013, Volume 115, Issue 4, pp 397-404 [link] [arxivpdf]
Non integrability of a self-gravitating Riemann liquid ellipsoid
Thierry Combot
Regular and Chaotic Dynamics, September 2013, Volume 18, Issue 5, pp 497-507 [link] [arxivpdf]
Integrability conditions at order 2 for homogeneous potentials of degree -1
Thierry Combot
Nonlinearity 2013, 26, 95 [link] [arxivpdf]
Third order integrability conditions for homogeneous potentials of degree -1
Thierry Combot and Christoph Koutschan
Journal of Mathematical Physics 2012, 53, 082704 [link] [arxivpdf]
Non-integrability of the equal mass n-body problem with non-zero angular momentum
Thierry Combot
Celestial Mechanics and Dynamical Astronomy December 2012, Volume 114, Issue 4, pp 319-340 [link] [arxivpdf]
Integrability conditions at order 2 for homogeneous potentials of degree -1
Alin Bostan and Thierry Combot
American Mathematical Monthly, Volume 119, Number 7, August-September 2012 , pp. 593-597(5) [link]