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Invariant algebraic curves of generalized Liénard polynomial differential systems
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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
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9 p, 596.2 KB |
A new sufficient condition in order that the real Jacobian conjecture in R2 holds
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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
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21 p, 476.1 KB |
Lower bounds for the local cyclicity for families of centers
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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
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Vanishing set of inverse Jacobi multipliers and attractor/repeller sets
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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
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