Browsing by Author "Llibre Saló, Jaume"

A new approach to the vakonomic mechanics
Llibre Saló, Jaume; Ramírez Ros, Rafael; Sadovskaia Nurimanova, Natalia Guennadievna (20141101)
Article
Restricted access  publisher's policyThe aim of this paper was to show that the Lagranged'Alembert and its equivalent the Gauss and Appel principle are not the only way to deduce the equations of motion of the nonholonomic systems. Instead of them we consider ... 
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. 
Axiomatic definition of the topological entropy on the interval
Alseda Soler, Lluís; Kolyada, Sergi; Llibre Saló, Jaume; Snoha, Lubomír (2000)
Article
Open AccessSummary. 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 ... 
Bifurcation of relative equilibria of the (1+3)body problem
Corbera, M.; Cors Iglesias, Josep Maria; Llibre Saló, Jaume; Moeckel, Richard (20150402)
Article
Open AccessWe study the relative equilibria of the limit case of the planar Newtonian 4body problem when three masses tend to zero, the socalled (1+3)body problem. Depending on the values of the infinitesimal masses the number of ... 
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 ... 
Central configurations of the planar coorbital satellite problem
Cors Iglesias, Josep Maria; Llibre Saló, Jaume; Ollé Torner, Mercè (2003)
Article
Open AccessWe 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 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 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 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 ... 
Horseshoe periodic orbits for saturn coorbital satellites
Llibre Saló, Jaume; Ollé Torner, Mercè (2000)
Article
Open AccessWe consider the motion of coorbital satellites in the framework of the Restricted ThreeBody 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 
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 the 16th Hilbert problem for algebraic limit cycles
Llibre Saló, Jaume; Ramírez Inostroza, Rafael Orlando; Sadovskaia Nurimanova, Natalia Guennadievna (20100315)
Article
Restricted access  publisher's policyFor 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 (20110115)
Article
Restricted access  publisher's policyWe 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 AccessWe 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 threebody 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 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 ...