Now showing items 1-16 of 16

  • 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.
  • Axiomatic definition of the topological entropy on the interval 

    Alseda Soler, Lluís; Kolyada, Sergi; Llibre Saló, Jaume; Snoha, Lubomír (2000)
    Article
    Open Access
    Summary. The aim of this paper is to give an axiomatic definition of the topological entropy for continuous interval maps and, in such a way, to shed some more light on the importance of the different properties of the ...
  • Central configurations of the planar coorbital satellite problem 

    Cors Iglesias, Josep Maria; Llibre Saló, Jaume; Ollé Torner, Mercè (2003)
    Article
    Open Access
    We study the planar central configurations of the 1 + n body problem where one mass is large and the other n masses are infinitesimal and equal. We find analytically all these central configurations when 2 ≤ n ≤ 4. Numerically, ...
  • 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 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 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 ...
  • Horseshoe periodic orbits for saturn coorbital satellites 

    Llibre Saló, Jaume; Ollé Torner, Mercè (2000)
    Article
    Open Access
    We consider the motion of coorbital satellites in the framework of the Restricted Three-Body problem for u=6.5*10^(-9). We show a mechanism to generate horsehoe periodic orbits and we compute some families of horseshoe ...
  • Horseshoe periodic orbits in the restricted three body problem 

    Llibre Saló, Jaume; Ollé Torner, Mercè (2001)
    Article
    Open Access
  • 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 ...
  • On the 16th Hilbert problem for algebraic limit cycles 

    Llibre Saló, Jaume; Ramírez Inostroza, Rafael Orlando; Sadovskaia Nurimanova, Natalia Guennadievna (2010-03-15)
    Article
    Restricted access - publisher's policy
    For a polynomial planar vector field of degree n ≥ 2 with generic invariant algebraic curves we show that the maximum number of algebraic limit cycles is 1 + (n − 1)(n − 2)/2 when n is even, and (n − 1)(n − 2)/2 when n is ...
  • On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves 

    Llibre Saló, Jaume; Ramírez Inostroza, Rafael Orlando; Sadovskaia Nurimanova, Natalia Guennadievna (2011-01-15)
    Article
    Restricted access - publisher's policy
    We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial vector field of degree n can exhibit if the vector field has exactly k nonsingular irreducible invariant algebraic curves. ...
  • On the central configurations of the planar 1 + 3 body problem 

    Corbera, M.; Cors Iglesias, Josep Maria; Llibre Saló, Jaume (2011)
    Article
    Open Access
    We consider the Newtonian 4 body problem in the plane with a dominat mass M. We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two diferent classes of central ...
  • Periodic orbits of horseshoe type in the planar restricted three-body problem 

    Llibre Saló, Jaume; Ollé Torner, Mercè (2002)
    Article
    Open Access
  • 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 ...
  • The motion of Saturn coorbital satellites in the restricted three-body problem 

    Llibre Saló, Jaume; Ollé Torner, Mercè (2001)
    Article
    Open Access
    This paper provides a description of the motion of Saturn coorbital satellites Janus and Epimetheus by means of horseshoe periodic orbits in the framework of the planar restricted three-body problem for the mass parameter ...