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Normal Forms for Polynomial Differential Systems in R-3 Having an Invariant Quadric and a Darboux Invariant
(World Scientific Publ Co Pte Ltd, 2015)
Darboux integrability for polynomial vector fields invariant under action of finite group
(Qualitative Theory of Dynamical Systems, 2018)
Darboux–Jouanolou–Ghys integrability for one-dimensional foliations on toric varieties
(Bulletin des Sciences Mathématiques, 2018)
Darboux-Egoroff metrics, rational Landau-Ginzburg potentials and the Painleve VI equation
(Iop Publishing Ltd, 2003-01-31)
We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational ...
On the dynamics of the Bianchi IX system
(Iop Publishing Ltd, 2007-06-29)
In this paper, we study the flow on three invariant sets of dimension five for the classical Bianchi IX system. In these invariant sets, using the Darboux theory of integrability, we prove the non-existence of periodic ...