Now showing items 1-20 of 20

    • 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 policy
      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)
      Article
      Restricted access - publisher's policy
      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)
      Article
      Open Access
      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 dynamics of the Basener–Ross population model 

      Güngör, Faruk; Llibre Saló, Jaume; Pantazi, Chara (Circolo Matematico di Palermo, 2020)
      Article
      Open Access
      We 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 Access
      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 (2011-11-01)
      External research report
      Open Access
      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 integrals for Schrödinger planar vector fields via Darboux transformations 

      Acosta Humánez, Primitivo Belén; Pantazi, Chara (2012-07-14)
      Article
      Open Access
      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 theory of integrability for a class of nonautonomous vector fields 

      Llibre Saló, Jaume; Pantazi, Chara (2009-10)
      Article
      Open Access
      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)
      Article
      Restricted access - publisher's policy
      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)
      Article
      Open Access
      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)
      External research report
      Open Access
      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)
      Article
      Open Access
      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 planar polynomial vector fields with elementary first integrals 

      Christopher, Colin; Pantazi, Chara; Llibre Saló, Jaume; Walcher, Sebastian (2019-10-05)
      Article
      Restricted access - publisher's policy
      We 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 Picard-Vessiot theory 

      Lázaro Ochoa, José Tomás; Morales Ruíz, Juan José; Acosta Humánez, Primitivo Belén; Pantazi, Chara (2012-01-12)
      External research report
      Open Access
      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)
      Article
      Open Access
      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)
      Conference report
      Open Access
      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)
      Article
      Open Access
      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)
      External research report
      Restricted access - publisher's policy
      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)
      Article
      Open Access
      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)
      Article
      Open Access
      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 ...