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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, 2015-01-01)
We give the normal forms of all polynomial differential systems in R-3 which have a nondegenerate or degenerate quadric as an invariant algebraic surface. We also characterize among these systems those which have a Darboux ...
Darboux invariants for planar polynomial differential systems having an invariant conic
(Springer, 2014-12-01)
We characterize all the planar polynomial differential systems with a unique invariant algebraic curve given by a real conic and having a Darboux invariant.
Nonchaotic Behavior in Quadratic Three-Dimensional Differential Systems with a Symmetric Jacobian Matrix
(2018-03-01)
In this paper, we give an algebraic criterion to determine the nonchaotic behavior for polynomial differential systems defined in ℝ3 and, using this result, we give a partial positive answer for the conjecture about the ...
Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations
(World Scientific Publ Co Pte Ltd, 2020-06-30)
In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ...
Integrability and Dynamics of Quadratic Three-Dimensional Differential Systems Having an Invariant Paraboloid
(2016-07-01)
Invariant algebraic surfaces are commonly observed in differential systems arising in mathematical modeling of natural phenomena. In this paper, we study the integrability and dynamics of quadratic polynomial differential ...
On the integrability and the zero-Hopf bifurcation of a Chen-Wang differential system
(SpringerDordrecht, 2015-04)
The first objective of this paper was to study the Darboux integrability of the polynomial differential system
'X PONTO' = y, 'Y PONTO' = z, 'Z PONTO' = −y − 'X POT.2' − xz + 3'Y POT.2' + a,
and the second one is to ...
Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces
(2018-03-01)
In this paper we give the normal form of all polynomial differential systems in R3 having a weighted homogeneous surface f= 0 as an invariant algebraic surface and characterize among these systems those having a Darboux ...
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 ...
Hexagonal Geodesic 3-Webs
(Oxford Univ Press, 2021-08-01)
We prove that a surface carries a hexagonal 3-web of geodesics if and only if the geodesic flow on the surface admits a cubic 1st integral and show that the system of partial differential equations, governing metrics on ...