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Artículos, Encontrados 28 registros
Artículos Encontrados 28 registros  1 - 10siguientefinal  ir al registro:
1.
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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2.
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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3.
17 p, 655.4 KB Dynamics and Darboux integrability of the D 2 polynomial vector fields of degree 2 in ℝ3 / Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon. Centre de Physique Théorique (France)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
We characterize the Darboux integrability and the global dynamics of the 3-dimensional polynomial differential systems of degree 2 which are invariant under the D2 symmetric group, which have been partially studied previously by several authors.
2021 - 10.1007/s11040-020-09372-0
Mathematical Physics, Analysis and Geometry, Vol. 24, Issue 1 (March 2021) , art. 1  
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4.
17 p, 394.2 KB Nilpotent saddles of linear plus cubic homogeneous polynomial reversible vector fields / Corbera Subirana, Montserrat (Universitat de Vic - Universitat Central de Catalunya) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica (Portugal))
We provide normal forms and the global phase portraits in the Poincaré disk for all planar polynomial vector fields of the form lineal plus cubic homogeneous that are symmetric with respect to the x-axis or to the y-axis and having a nilpotent saddle at the origin.
2020 - 10.1016/j.bulsci.2020.102873
Bulletin des Sciences Mathematiques, Vol. 162 (September 2020) , art. 102873  
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5.
7 p, 613.2 KB On the limit cycles surrounding a diagonalizable linear node with homogeneous nonlinearities / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Salhi, Tayeb (Université de Bordj Bou Arréridj. Departement de Mathématiques (Algeria))
In this paper we study the existence and non-existence of limit cycles for the class of polynomial differential systems of the form ẋ=λx+Pn(x,y),ẏ=μy+Qn(x,y),where Pn and Qn are homogeneous polynomials of degree n.
2019 - 10.1016/j.aml.2019.07.002
Applied Mathematics Letters, Vol. 98 (December 2019) , p. 427-431  
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6.
9 p, 281.5 KB Bounded polynomial vector fields in R2 and Rn / Barreira, Luis (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We characterize the bounded polynomial vector fields in R2. Additionally we provide a necessary condition but not sufficient which must be satisfied by bounded polynomial vector fields in Rn.
2020 - 10.1016/j.jde.2019.10.023
Journal of differential equations, Vol. 268, Issue 8 (April 2020) , p. 4416-4422  
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7.
21 p, 626.8 KB Phase portraits for some symmetric cubic Riccati polynomial differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de São Paulo. Departamento de Matemática) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)
We classify the topological phase portraits in the Poincaré disc of two classes of symmetric Riccati cubic polynomial differential systems.
2018 - 10.1016/j.topol.2017.11.023
Topology and its applications, Vol. 234 (Feb. 2018) , p. 220-237  
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8.
15 p, 348.8 KB Global phase portraits for the Abel quadratic polynomial differential equations of second kind with Z₂-symmetries / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)
We provide normal forms and the global phase portraits in the Poincaré disk for all Abel quadratic polynomial differential equations of the second kind with Z₂-symmetries.
2018 - 10.4153/CMB-2017-026-6
Canadian mathematical bulletin, Vol. 61, issue 1 (2018) , p. 149-165  
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9.
36 p, 1.2 MB Linear type centers of polynomial Hamiltonian systems with nonlinearities of degree 4 symmetric with respect to the y-axis / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Martínez, Y. Paulina (Universidad del Bío-Bío. Departamento de Matemática) ; Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)
We provide normal forms and the phase portraits in the Poincaré disk for all the linear type centers of polynomial Hamiltonian systems with nonlinearities of degree 4 symmetric with respect to the y-axis.
2018 - 10.3934/dcdsb.2018047
Discrete and continuous dynamical systems. Series B, Vol. 23, issue 2 (2018) , p. 887-912  
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10.
7 p, 170.1 KB Normal forms and hyperbolic algebraic limit cycles for a class of polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàticaa)
We study the normal forms of polynomial systems having a set of invariant algebraic curves with singular points. We provide sufficient conditions for the existence of hyperbolic algebraic limit cycles.
2018
Electronic journal of differential equations, Vol. 2018, no. 83 (2018) , p. 1-7  
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Artículos : Encontrados 28 registros   1 - 10siguientefinal  ir al registro:
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