Dipòsit Digital de Documents de la UAB 54 registres trobats  1 - 10següentfinal  anar al registre: La cerca s'ha fet en 0.01 segons. 
1.
A new sufficient condition in order that the real Jacobian conjecture in R2 holds / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Let F = (f,g) : R2 → R2 be a polynomial map such that det⁡(DF(x,y)) is nowhere zero and F(0,0) = (0,0). In this work we give a new sufficient condition for the injectivity of F. We also state a conjecture when det⁡(DF(x,y)) = constant ≠ 0 and F(0,0) = (0,0) equivalent to the Jacobian conjecture.
2021 - 10.1016/j.jde.2021.01.038
Journal of differential equations, Vol. 281 (April 2021) , p. 333-340  
2.
Lower bounds for the local cyclicity for families of centers / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Gouveia, Luiz F. S (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we are interested on how the local cyclicity of a family of centers depends on the parameters. This fact, was pointed out in [21], to prove that there exists a family of cubic centers, labeled by CD12 31 in [25], with more local cyclicity than expected. [...]
2021 - 10.1016/j.jde.2020.11.035
Journal of differential equations, Vol. 275 (February 2021) , p. 309-331  
3.
19 p, 1.5 MB Vanishing set of inverse Jacobi multipliers and attractor/repeller sets / García, Isaac A. (Universitat de Lleida. Departament de Matemàtica) ; Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Maza, Susanna (Universitat de Lleida. Departament de Matemàtica)
In this paper, we study conditions under which the zero-set of the inverse Jacobi multiplier of a smooth vector field contains its attractor/repeller compact sets. The work generalizes previous results focusing on sink singularities, orbitally asymptotic limit cycles, and monodromic attractor graphics. [...]
2021 - 10.1063/5.0020360
Chaos, Vol. 31, Issue 1 (January 2021) , art. 13113  
4.
12 p, 664.4 KB Formal Weierstrass nonintegrability criterion for some classes of polynomial differential systems in C² / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we present a criterion for determining the formal Weierstrass nonintegrability of some polynomial differential systems in the plane C². The criterion uses solutions of the form y = f(x) of the differential system in the plane and their associated cofactors, where f(x) is a formal power series. [...]
2020 - 10.1142/S0218127420500649
International Journal of Bifurcation and Chaos, Vol. 30, Issue 4 (March 2020) , art. 2050064  
5.
15 p, 767.1 KB On the mechanisms for producing linear type centers in polynomial differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the different mechanisms that give rise to linear type centers for polynomial differential systems. The known mechanisms are the algebraic reversibility and the Liouville integrability. [...]
2018
Moscow Mathematical Journal, Vol. 18, Issue 3 (July-September 2018) , p. 409-420  
6.
9 p, 686.4 KB Chiellini Hamiltonian Liénard differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We characterize the centers of the Chiellini Hamiltonian Liénard second-order differential equations x' = y, y' = −f(x)y−g(x) where g(x) = f(x)(k−α(1 + α)Rf(x)dx) with α,k ∈ R. Moreover we study the phase portraits in the Poincaré disk of these systems when f(x) is linear.
2019
Electronic journal of differential equations, Vol. 2019, Issue 71 (2019) , p. 1-8
2 documents
7.
19 p, 716.5 KB Strongly formal weierstrass non-integrability for polynomial differential systems in C2 / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica.) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Recently a criterion has been given for determining the weakly formal Weierstrass non-integrability of polynomial differential systems in C2. Here we extend this criterion for determining the strongly formal Weierstrass non-integrability which includes the weakly formal Weierstrass non-integrability of polynomial differential systems in C2. [...]
2020 - 10.14232/ejqtde.2020.1.1
Electronic Journal of Qualitative Theory of Differential Equations, Vol. 2020, Issue 1 (2020) , p. 1-16
2 documents
8.
12 p, 673.9 KB Highest weak focus order for trigonometric Liénard equations / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
Given a planar analytic differential equation with a critical point which is a weak focus of order k, it is well known that at most k limit cycles can bifurcate from it. Moreover, in case of analytic Liénard differential equations this order can be computed as one half of the multiplicity of an associated planar analytic map. [...]
2019 - 10.1007/s10231-019-00936-8
Annali di Matematica Pura ed Applicata, (November 2019)  
9.
16 p, 322.4 KB The center problem for Z2-symmetric nilpotent vector fields / Algaba, Antonio (Universidad de Huelva. Departamento de Matemáticas) ; García, Cristóbal (Universidad de Huelva. Departamento de Matemáticas) ; Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We say that a polynomial differential system x˙=P(x,y), y˙=Q(x,y) having the origin as a singular point is Z-symmetric if P(−x,−y)=−P(x,y) and Q(−x,−y)=−Q(x,y). It is known that there are nilpotent centers having a local analytic first integral, and others which only have a C first integral. [...]
2018 - 10.1016/j.jmaa.2018.05.079
Journal of mathematical analysis and applications, Vol. 466, Issue 1 (October 2018) , p. 183-198  
10.
Orbitally universal centers / Algaba, Antonio (Universidad de Huelva. Departamento de Matemáticas) ; García, Cristóbal (Universidad de Huelva. Departamento de Matemáticas) ; Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we define when a polynomial differential system is orbitally universal and we show the relevance of this notion in the classical center problem, i. e. in the problem of distinguishing between a focus and a center.
2020 - 10.1016/j.na.2020.111746
Nonlinear Analysis : Theory, Methods and Applications, Vol. 195 (June 2020) , art. 111746  

Dipòsit Digital de Documents de la UAB : 54 registres trobats   1 - 10següentfinal  anar al registre:
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