• Analytic integrability of Bianchi Class A cosmological models with k=1 

    Ferragut Amengual, Antoni Manel; Llibre Saló, Jaume; Pantazi, Chara (2012)
    Artículo
    Acceso restringido por política de la editorial
    We 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 quasi-homogeneous polynomial differential equations of degree three 

    Aziz, Waleed; Llibre Saló, Jaume; Pantazi, Chara (2014-03-20)
    Artículo
    Acceso restringido por política de la editorial
    We characterize the centers of the quasi-homogeneous 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)
    Artículo
    Acceso abierto
    In 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 invariant algebraic curves for planar polynomial systems 

    Christopher, C.; Llibre Saló, Jaume; Pantazi, Chara; Zhang, Xiang (2004)
    Artículo
    Acceso abierto
    In 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 (2012-07-14)
    Artículo
    Acceso abierto
    In 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 integrals for Schrödinger planar vector fields via Darboux transformations 

    Acosta Humánez, Primitivo Belén; Pantazi, Chara (2011-11-01)
    Report de recerca
    Acceso abierto
    In 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 theory of integrability for a class of nonautonomous vector fields 

    Llibre Saló, Jaume; Pantazi, Chara (2009-10)
    Artículo
    Acceso abierto
    The 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 non-integrability of planar polynomial vector fields 

    Lázaro Ochoa, José Tomás; Pantazi, Chara; Acosta Humanez, Primitivo; Morales Ruiz, Juan José (2018-02-26)
    Artículo
    Acceso restringido por política de la editorial
    We 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 (2016-02-01)
    Artículo
    Acceso abierto
    We 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 (2011-11-03)
    Report de recerca
    Acceso abierto
    In 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 (2013-12)
    Artículo
    Acceso abierto
    Polynomial vector fields which admit a prescribed Darboux integrat- ing factor are quite well-understood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane ...
  • On the integrability of polynomial fields in the plane by means of Picard-Vessiot theory 

    Lázaro Ochoa, José Tomás; Morales Ruíz, Juan José; Acosta Humánez, Primitivo Belén; Pantazi, Chara (2012-01-12)
    Report de recerca
    Acceso abierto
    We 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 Picard-Vessiot theory 

    Acosta-Humànez, Primitivo; Lázaro Ochoa, José Tomás; Morales Ruiz, Juan José; Pantazi, Chara (American Institute of Mathematical Sciences, 2015-05-01)
    Artículo
    Acceso abierto
    We 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, 2007-09)
    Texto en actas de congreso
    Acceso abierto
    We 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)
    Artículo
    Acceso abierto
    The 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 (2011-07-06)
    Report de recerca
    Acceso restringido por política de la editorial
    The 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)
    Artículo
    Acceso abierto
    We 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 Picard-Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system 

    Fedorov, Yuri; Pantazi, Chara (2014-03-01)
    Artículo
    Acceso abierto
    We 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 ...