Dipòsit Digital de Documents de la UAB 58 registres trobats  1 - 10següentfinal  anar al registre: La cerca s'ha fet en 0.00 segons. 
1.
16 p, 265.2 KB Time-reversibility and integrability of p : −q resonant vector fields / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Romanovski, Valery G. (University of Maribor. Center for Applied Mathematics and Theoretical Physics) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the local analytical integrability in a neighborhood of p: −q resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect to the non-smooth involution ϕ(x, y) = (yp/q, xq/p). [...]
2024 - 10.3934/math.2024005
AIMS Mathematics, Vol. 9, Issue 1 (2024) , p. 73-88  
2.
35 p, 627.1 KB Criteria on the existence of limit cycles in planar polynomial differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Grau, Maite (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We summarize known criteria for the non-existence, existence and on the number of limit cycles of autonomous real planar polynomial differential systems, and also provide new results. We give examples of systems which realize the maximum number of limit cycles provided by each criterion. [...]
2022 - 10.1016/j.exmath.2022.09.002
Expositiones Mathematicae, Vol. 40, Issue 4 (December 2022) , p. 1049-1083  
3.
4 p, 307.7 KB A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The generalized Liénard polynomial differential systems are the differential systems of the form x' = y, y' = − f(x)y − g(x), where f and g are polynomials. We characterize all the generalized Liénard polynomial differential systems having an invariant algebraic curve. [...]
2022 - 10.1016/j.chaos.2022.112075
Chaos, solitons and fractals, Vol. 158 (May 2022) , art. 112075
2 documents
4.
5 p, 244.9 KB Invariant algebraic curves of generalized Liénard polynomial differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this study, we focus on invariant algebraic curves of generalized Liénard polynomial differential systems x'= y, y'= −fm (x) y − gn (x), where the degrees of the polynomials f and g are m and n, respectively, and we correct some results previously stated.
2022 - 10.3390/math10020209
Mathematics, Vol. 10, Issue 2 (January 2022) , art. 209
2 documents
5.
9 p, 596.2 KB 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  
6.
21 p, 476.1 KB Lower bounds for the local cyclicity for families of centers / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Gouveia, Luiz Fernando (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  
7.
19 p, 1.5 MB Vanishing set of inverse Jacobi multipliers and attractor/repeller sets / García, Isaac (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  
8.
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 in applied sciences and engineering, Vol. 30, Issue 4 (March 2020) , art. 2050064  
9.
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  
10.
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

Dipòsit Digital de Documents de la UAB : 58 registres trobats   1 - 10següentfinal  anar al registre:
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54 Gine, Jaume
54 Giné, Jaume
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