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On the computation of Darboux first integrals of a class of planar polynomial vector fields
We study the class of planar polynomial vector fields admitting Darboux first integrals of the type ∏i=1 rfi αi, where the αi's are positive real numbers and the fi's are polynomials defining curves with only one place at ...
WDVV equations, Darboux-egoroff metric and the dressing method
(2002-01-01)
Dressing technique is used to construct commuting Lax operators which provide an integrable (canonical) structure behind Witten–Dijkgraaf–Verlinde–Verlinde equations. The commuting flows are related to the isomonodromic ...
On the Bäcklund and Darboux transformations for the Tzitzéica model
(Universidade Estadual Paulista (UNESP), 2014)
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 ...
Fator integrante inverso e suas aplicações
(Universidade Estadual Paulista (Unesp), 2021-03-15)
Este trabalho é dedicado ao estudo do fator integrante inverso de sistemas diferenciais planares. O fator integrante inverso está principalmente relacionado à solução do problema de integrabilidade de campo de vetores ...
Integral de Riemann no Rn
(2012)
Dynamical and algebraic analysis of planar polynomial vector fields linked to orthogonal polynomials
(Southwest Jiaotong University, 2020-08)
In the present work, our goal is to establish a study of some families of quadratic polynomial vector fields connected to orthogonal polynomials that relate, via two different points of view, the qualitative and the algebraic ...
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 ...
Darboux–Jouanolou–Ghys integrability for one-dimensional foliations on toric varieties
(Bulletin des Sciences Mathématiques, 2018)