Browsing by Author "Pantazi, Chara"
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Analytic integrability of Bianchi Class A cosmological models with k=1
Ferragut Amengual, Antoni Manel; Llibre Saló, Jaume; Pantazi, Chara (2012)
Article
Restricted access  publisher's policyWe complete the study of the analytic integrability of the Class A of Bianchi cosmological models with k=1, characterizing the analytic first integrals of the Bianchi types V I0 and V III0. 
Centers of quasihomogeneous polynomial differential equations of degree three
Aziz, Waleed; Llibre Saló, Jaume; Pantazi, Chara (20140320)
Article
Restricted access  publisher's policyWe characterize the centers of the quasihomogeneous planar polynomial differential systems of degree three. Such systems do not admit isochronous centers. At most one limit cycle can bifurcate from the periodic orbits of ... 
Counterexample to a conjecture on the algebraic limit cycles of polynomial vector fields
Llibre Saló, Jaume; Pantazi, Chara (2004)
Article
Open AccessIn Geometriae Dedicata 79 (2000), 101{108, Rudolf Winkel conjectured: For a given algebraic curve f = 0 of degree m > 4 there is in general no polynomial vector ¯eld of degree less than 2m ¡ 1 leaving invariant f = 0 ... 
Darboux integrability and dynamics of the Basener–Ross population model
Güngör, Faruk; Llibre Saló, Jaume; Pantazi, Chara (Circolo Matematico di Palermo, 2020)
Article
Open AccessWe deal with the Basener and Ross model for the evolution of human population in Easter island. We study the Darboux integrability of this model and characterize all its global dynamics in the Poincaré disc, obtaining 15 ... 
Darboux integrability and invariant algebraic curves for planar polynomial systems
Christopher, C.; Llibre Saló, Jaume; Pantazi, Chara; Zhang, Xiang (2004)
Article
Open AccessIn this paper we study the normal forms of polynomial systems having a set of given generic invariant algebraic curves. 
Darboux integrals for Schrödinger planar vector fields via Darboux transformations
Acosta Humánez, Primitivo Belén; Pantazi, Chara (20111101)
External research report
Open AccessIn this paper we study the Darboux transformations of planar vector fields of Schrödinger type. Using the isogaloisian property of Darboux transformation we prove the “invariance” of the elements of the “Darboux Theory of ... 
Darboux integrals for Schrödinger planar vector fields via Darboux transformations
Acosta Humánez, Primitivo Belén; Pantazi, Chara (20120714)
Article
Open AccessIn this paper we study the Darboux transformations of planar vector fields of Schr odinger type. Using the isogaloisian property of Darboux transformation we prove the \invariance" of the objects of the \Darboux theory ... 
Darboux theory of integrability for a class of nonautonomous vector fields
Llibre Saló, Jaume; Pantazi, Chara (200910)
Article
Open AccessThe goal of this paper is to extend the classical Darboux theory of integrability from autonomous polynomial vector fields to a class of nonautonomous vector fields. We also provide sufficient conditions for applying ... 
Differential galois theory and nonintegrability of planar polynomial vector fields
Lázaro Ochoa, José Tomás; Pantazi, Chara; Acosta Humanez, Primitivo; Morales Ruiz, Juan José (20180226)
Article
Restricted access  publisher's policyWe study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular ... 
Limit cycles bifurcating from a degenerate center
Llibre Saló, Jaume; Pantazi, Chara (20160201)
Article
Open AccessWe study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of ... 
Morphisms and inverse problems
Christopher, Colin; Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (20111103)
External research report
Open AccessIn order to investigate polynomial vector ¯elds admitting a prescribed Darboux integrating factor, we show that it is helpful to employ morphisms of the a±ne plane. In particular, such morphisms may be used to remove ... 
Morphisms and inverse problems for Darboux integrating factors
Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (201312)
Article
Open AccessPolynomial vector fields which admit a prescribed Darboux integrat ing factor are quite wellunderstood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane ... 
On planar polynomial vector fields with elementary first integrals
Christopher, Colin; Pantazi, Chara; Llibre Saló, Jaume; Walcher, Sebastian (20191005)
Article
Restricted access  publisher's policyWe show that under rather general conditions a polynomial differential system having an elementary first integral already must admit a Darboux first integral, and we explicitly characterize the vector fields in this class. ... 
On the integrability of polynomial fields in the plane by means of PicardVessiot theory
Lázaro Ochoa, José Tomás; Morales Ruíz, Juan José; Acosta Humánez, Primitivo Belén; Pantazi, Chara (20120112)
External research report
Open AccessWe study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results ... 
On the integrability of polynomial vector fields in the plane by means of PicardVessiot theory
AcostaHumànez, Primitivo; Lázaro Ochoa, José Tomás; Morales Ruiz, Juan José; Pantazi, Chara (American Institute of Mathematical Sciences, 20150501)
Article
Open AccessWe study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results ... 
Phase portraits of separable Hamiltonian systems
Guillamon Grabolosa, Antoni; Pantazi, Chara (Universidad de Sevilla, 200709)
Conference report
Open AccessWe study some generalizations of potential Hamiltonian systems $(H(x, y) = y^2 + F(x))$ with one degree of freedom. In particular, we are interested in Hamiltonian systems with Hamiltonian functions of type $H(x, y) = ... 
Polynomial differential systems having a given Darbouxian first integral
Llibre Saló, Jaume; Pantazi, Chara (Elsevier, 2004)
Article
Open AccessThe Darbouxian theory of integrability allows to determine when a polynomial differential system in C2 has a first integral of the kind f λ1 1 ···f λp p exp(g/h) where fi , g and h are polynomials in C[x, y], and λi ∈ C ... 
Some inverse problems
Christopher, Colin; Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (20110706)
External research report
Restricted access  publisher's policyThe Darboux theory of integrability for planar polynomial di®erential equations is a classical ¯eld, with connections to Lie symmetries, di®erential algebra and other areas of mathematics. In the present paper we introduce ... 
Symmetries of homogeneous cosmologies
Cotsakis, Spiros; Leach, P. G. L.; Pantazi, Chara (2004)
Article
Open AccessWe reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self interaction potential in the language of jet bundles and extensions of vector fields. In this framework, the ... 
The PicardFuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system
Fedorov, Yuri; Pantazi, Chara (20140301)
Article
Open AccessWe consider a family of genus 2 hyperelliptic curves of even order and obtain explicitly the systems of 5 linear ordinary differential equations for periods of the corresponding Abelian integrals of first, second, and third ...