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Articles, 42 registres trobats
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Articles 42 registres trobats  1 - 10següentfinal  anar al registre:
1.
Critical periods in planar polynomial centers near a maximum number of cusps / De Maesschalck, Peter (Hasselt University) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide the best lower bound for the number of critical periods of planar polynomial centers known up to now. The new lower bound is obtained in the Hamiltonian class and considering a single period annulus. [...]
2024 - 10.1016/j.jde.2023.10.034
Journal of differential equations, Vol. 380 (January 2024) , p. 181-197  
2.
7 p, 289.7 KB A remark on first integrals of vector fields / Belotto da Silva, André (Université de Paris, Institut de Mathématiques de Jussieu Paris Rive Gauche) ; Klimeš, Martin (University of Zagreb. Faculty of Electrical Engineering and Computing) ; Rebelo, Julio (Institut de Mathématiques de Toulouse) ; Reis, Helena (Universidade do Porto. Centro de Matemática)
We provide examples of vector fields on (C3 , 0) admitting a formal first integral but no holomorphic first integral. These examples are related to a question raised by D. Cerveau and motivated by the celebrated theorems of Malgrange and Mattei-Moussu.
2024 - 10.5565/PUBLMAT6812405
Publicacions matemàtiques, Vol. 68 Núm. 1 (2024) , p. 103-109 (Articles)  
3.
On the indices of singular points for planar bounded piecewise smooth polynomial vector field / Li, Shimin (Hangzhou Normal University. School of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Sun, Xianbo (Hangzhou Normal University. School of Mathematics)
We prove that for any piecewise-smooth bounded polynomial vector field in R2 with finitely many finite H-singular points (which include singular points, hyperbolic pseudo-equilibria and two fold singularities), the sum of the indices of all its finite H-singular points is 1.
2023 - 10.1016/j.nahs.2023.101350
Nonlinear Analysis: Hybrid Systems, Vol. 49 (August 2023) , art. 101350  
4.
12 p, 781.7 KB Limit cycles of a perturbation of a polynomial Hamiltonian systems of degree 4 symmetric with respect to the origin / 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 study the number of limit cycles bifurcating from the origin of a Hamiltonian system of degree 4. We prove, using the averaging theory of order 7, that there are quartic polynomial systems close these Hamiltonian systems having 3 limit cycles.
2020 - 10.4153/S0008439519000626
Canadian mathematical bulletin, Vol. 63, Issue 3 (September 2020) , p. 547-561  
5.
21 p, 949.4 KB Limit cycles on piecewise smooth vector fields with coupled rigid centers / Carvalho, Tiago (Universidade de São Paulo. Departamento de Computação e Matemática) ; Gonçalves, Luiz Fernando (Universidade Federal de Goiás. Instituto de Matemática e Estatística) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide an upper bound for the maximum number of limit cycles of the class of discontinuous piecewise differential systems formed by two differential systems separated by a straight line presenting rigid centers. [...]
2021 - 10.1142/S0218127421502242
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 31, Issue 15 (December 2021) , art. 2150224  
6.
13 p, 663.8 KB Phase portraits of uniform isochronous centers with homogeneous nonlinearities / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
We classify the phase portraits in the Poincaré disc of the differential equations of the form x' = − y + xf(x, y), ẏ = x + yf(x, y) where f(x,y) is a homogeneous polynomial of degree n − 1 when n = 2, 3, 4, 5, and f has only simple zeroes. [...]
2021 - 10.1007/s10883-021-09529-2
Journal of Dynamical and Control Systems, Vol. 28 (February 2021) , p. 319-332  
7.
8 p, 299.6 KB Polynomial vector fields on the Clifford torus / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Murza, Adrian C. (University of Texas at Dallas. Department of Mathematical Sciences (USA))
First, we characterize all the polynomial vector fields in R4 which have the Clifford torus as an invariant surface. Then we study the number of invariant meridians and parallels that such polynomial vector fields can have on the Clifford torus as a function of the degree of these vector fields.
2021 - 10.1142/S0218127421500577
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 31, Issue 4 (March 2021) , art. 2150057  
8.
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  
9.
21 p, 356.4 KB Local cyclicity in low degree planar piecewise polynomial vector fields / Gouveia, Luiz Fernando (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small amplitude. [...]
2021 - 10.1016/j.nonrwa.2020.103278
Nonlinear Analysis: Real World Applications, Vol. 60 (August 2021) , art. 103278  
10.
30 p, 468.7 KB Lower bounds for the local cyclicity of centers using high order developments and parallelization / Gouveia, Luiz Fernando (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We are interested in small-amplitude isolated periodic orbits, so-called limit cycles, surrounding only one equilibrium point, that we locate at the origin. We develop a parallelization technique to study higher order developments, with respect to the parameters, of the return map near the origin. [...]
2021 - 10.1016/j.jde.2020.08.027
Journal of differential equations, Vol. 271 (January 2021) , p. 447-479  

Articles : 42 registres trobats   1 - 10següentfinal  anar al registre:
Documents de recerca 1 registres trobats  
1.
129 p, 1.1 MB Hamiltonian linear type centers and nilpotent centers of linear plus cubic polynomial vector fields / Colak, Ilker Evrim ; Llibre, Jaume, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia, 1973-, dir. ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
En este trabajo proporcionamos doce formas normales para todos los campos vectoriales polinomiales Hamiltonianos en el plano que tienen términos lineales más cúbicos homogéneos y que poseen en el origen un centro de tipo lineal o un centro nilpotente. [...]
In this work we provide twelve normal forms for all the Hamiltonian planar polynomial vector fields having linear plus cubic homogeneous terms which possess a linear type center or a nilpotent center at the origin, and find their global phase portraits on the Poincaré disk. [...]

[Barcelona] : Universitat Autònoma de Barcelona, 2014  

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