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Dipòsit Digital de Documents de la UAB 52 registres trobats  1 - 10següentfinal  anar al registre: La cerca s'ha fet en 0.01 segons. 
1.
19 p, 397.7 KB Limit Cycles of Polynomially Integrable Piecewise Differential Systems / García, Belén (Universidad de Oviedo. Departamento de Matemáticas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pérez del Río, Jesús S. (Universidad de Oviedo. Departamento de Matemáticas) ; Pérez-González, Set (Universidad de Oviedo. Departamento de Matemáticas)
In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides. We assume that at least one of the systems is Hamiltonian. [...]
2023 - 10.3390/axioms12040342
Axioms, Vol. 12, Issue 4 (March 2023) , art. 342  
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2.
42 p, 672.9 KB The improved Euler-Jacobi formula and the planar cubic polynomial vector fields in ℝ2 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
The new Euler-Jacobi formula for points with multiplicity two provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have eight finite singular points, being one of them with multiplicity two. [...]
2022 - 10.1080/14689367.2022.2066508
Dynamical Systems, Vol. 37, Issue 3 (2022) , p. 403-443  
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3.
Characterization of the kukles polynomial differential systems having an invariant algebraic curve / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
Let f(x) and g(x) be complex polynomials. We characterize all Kukles polynomial differential systems of the form x = y, y = −y −f(x)y −g(x) having an invariant algebraic curve. We show that expanding an invariant algebraic curve of these differential systems as a polynomial in the variable y, the first four higher coefficients of the polynomial defining the invariant algebraic curve determine completely these Kukles systems. [...]
2023 - 10.1016/j.bulsci.2022.103224
Bulletin des Sciences Mathematiques, Vol. 182 (February 2023) , art. 103224  
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4.
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
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5.
21 p, 806.2 KB On a class of polynomial differential systems of degree 4 : Phase portraits and limit cycles / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Salhi, Tayeb (Université de Bordj Bou Arréridj. Département de Mathématiques (Algeria))
In this paper we characterize the phase portraits in the Poincaré disc of the class of polynomial differential systems of the form ẋ = −y, ẏ = x + ax4 + bx2 y2 + cy4, with a2 + b2 + c2 ≠ 0, which are symmetric with respect to the x-axis. [...]
2021 - 10.12775/TMNA.2020.042
Topological Methods in Nonlinear Analysis, Vol. 57, Issue 2 (June 2021) , p. 441-463  
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6.
11 p, 285.4 KB Twin polynomial vector fields of arbitrary degree / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
In this paper we study polynomial vector fields on C2 of degree larger than 2 with n2 isolated singularities. More precisely, we show that if two polynomial vector fields share n2−1 singularities with the same spectra (trace and determinant) and from these singularities n2−2 have the same positions, then both vector fields have identical position and spectra at all the singularities. [...]
2022 - 10.1007/s00574-021-00259-4
Bulletin of the Brazilian Mathematical Society, Vol. 53, Issue 1 (March 2022) , p. 295-306  
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7.
16 p, 433.0 KB Algebraic and topological classification of homogeneous quartic vector fields in the plane / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Y. Paulina (Universidad del Bío-Bío. Departamento de Matemática (Chile)) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática (Chile))
We provide canonical forms for the homogeneous polynomials of degree five. Then we characterize all the phase portraits in the Poincaré disk for all quartic homogeneous polynomial differential systems. [...]
2022 - 10.1007/s10231-021-01106-5
Annali di Matematica Pura ed Applicata, Vol. 201, Issue 1 (February 2022) , p. 37-55  
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8.
22 p, 833.4 KB On the birth and death of algebraic limit cycles in quadratic differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e Computação. Departamento de Matemática (Brazil)) ; Zhao, Yulin (Sun Yat-sen University. School of Mathematics (People's Republic of China))
In 1958 started the study of the families of algebraic limit cycles in the class of planar quadratic polynomial differential systems. In the present we known one family of algebraic limit cycles of degree 2 and four families of algebraic limit cycles of degree 4, and that there are no limit cycles of degree 3. [...]
2021 - 10.1017/S0956792520000145
European Journal of Applied Mathematics, Vol. 32, Issue 2 (April 2021) , p. 317-336  
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9.
14 p, 598.2 KB Configurations of the topological indices of the planar polynomial differential systems of degree (2, m) / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
Using the Euler-Jacobi formula there is a relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the polynomial differential systems x˙ = P(x, y), y˙ = Q(x, y) with degree of P equal to 2 and degree of Q equal to m when these systems have 2m finite singular points.
2021 - 10.1007/s00025-020-01322-0
Results in Mathematics, Vol. 76, Issue 1 (March 2021) , art. 21  
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10.
36 p, 651.2 KB On the singularities of the planar cubic polynomial differential systems and the Euler Jacobi formula / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
Using the Euler-Jacobi formula we obtain an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have nine finite singular points.
2020 - 10.1007/s12346-020-00435-9
Qualitative theory of dynamical systems, Vol. 19, Issue 3 (December 2020) , art. 96  
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