Exploració per autor "Llibre Saló, Jaume"
Ara es mostren els items 19-33 de 33
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Morphisms and inverse problems
Christopher, Colin; Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (2011-11-03)
Report de recerca
Accés obertIn 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
Accés obertPolynomial 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
Accés obertWe 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 16th Hilbert problem for algebraic limit cycles
Llibre Saló, Jaume; Ramírez Inostroza, Rafael Orlando; Sadovskaia Nurimanova, Natalia Guennadievna (2010-03-15)
Article
Accés restringit per política de l'editorialFor 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
Accés restringit per política de l'editorialWe 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
Accés obertWe 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
Accés obert -
Polynomial differential systems having a given Darbouxian first integral
Llibre Saló, Jaume; Pantazi, Chara (Elsevier, 2004)
Article
Accés obertThe 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 ... -
Quadratic planar differential systems with algebraic limit cycles via quadratic plane Cremona maps
Alberich Carramiñana, Maria; Ferragut Amengual, Antoni Manel; Llibre Saló, Jaume (Elsevier, 2021)
Article
Accés obertIn this paper we study the action of planar birational transformations, also known as plane Cremona maps, on quadratic planar differential systems. We provide geometrical characterizations of when a quadratic system is ... -
Qualitative study of a model with Rastall gravity
Pantazi, Chara; Llibre Saló, Jaume (2020-12-17)
Article
Accés obertWe consider the Rastall theory for the flat Friedmann-Robertson-Walker Universe filled with a perfect fluid that satisfies a linear equation of state. The corresponding dynamical system is a two dimensional system of ... -
Qualitative study of the Selkov model
Llibre Saló, Jaume; Pantazi, Chara (Elsevier, 2024-06-05)
Article
Accés obertThe Selkov oscillator was formulated in 1968 and now it is a classical model for studying the glycolysis. It is a differential system of two equations depending on two parameters in dimensionless variables. When the two ... -
Some inverse problems
Christopher, Colin; Llibre Saló, Jaume; Pantazi, Chara; Walcher, Sebastian (2011-07-06)
Report de recerca
Accés restringit per política de l'editorialThe 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
Accés obertThis 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 ... -
Three-dimensional Lotka–Volterra systems with 3:-1:2-resonance
Aziz, Waleed; Christopher, Colin; Llibre Saló, Jaume; Pantazi, Chara (2021-08)
Article
Accés obertWe study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka–Volterra differential systems with (3:- 1:2)-resonance. We give necessary and sufficient conditions on the parameters of ... -
Trapezoid central configurations
Corbera, Montserrat; Cors Iglesias, Josep Maria; Llibre Saló, Jaume; Perez Chavela, Ernesto (2019-04-01)
Article
Accés obertWe classify all planar four–body central configurations where two pairs of the bodies are on parallel lines. Using cartesian coordinates, we show that the set of four–body trapezoid central configurations with positive ...