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Articles 63 records found  beginprevious21 - 30nextend  jump to record: Search took 0.06 seconds. 
21.
25 p, 954.3 KB Polynomial Hamiltonian systems of degree 3 with nilpotent saddles / 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 Hamiltonian planar polynomial vector fields of degree 3 symmetric with respect to the x−axis having a nilpotent saddle at the origin.
2021 - 10.3934/dcdsb.2020225
Discrete and continuous dynamical systems. Series B, Vol. 26, Issue 6 (June 2021) , p. 3209-3233  
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22.
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  
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23.
49 p, 872.3 KB Structurally unstable quadratic vector fields of codimension two : families possessing either a cusp point or two finite saddle-nodes / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação (Brazil)) ; Rezende, Alex C. (Universidade Federal de São Carlos. Departamento de Matemática (Brazil))
The goal of this paper is to contribute to the classification of the phase portraits of planar quadratic differential systems according to their structural stability. Artés et al. (Mem Am Math Soc 134:639, 1998) proved that there exist 44 structurally stable topologically distinct phase portraits in the Poincaré disc modulo limit cycles in this family, and Artés et al. [...]
2020 - 10.1007/s10884-020-09871-2
Journal of dynamics and differential equations, vol. 33 (July 2020) p. 1779-1821  
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24.
12 p, 915.5 KB Phase portraits of the Higgins-Selkov system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mousavi, Marzieh (Isfahan University of Technology. Department of Mathematical Sciences (Iran))
In this paper we study the dynamics of the Higgins-Selkov system x˙=1−xyγ,y˙=αy(xyγ−1−1), where α is a real parameter and γ > 1 is an integer. We classify the phase portraits of this system for γ = 3,4,5,6, in the Poincaré disc for all the values of the parameter α. [...]
2021 - 10.3934/dcdsb.2021039
Discrete and continuous dynamical systems. Series B, Vol. 26 (2021)  
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25.
25 p, 548.4 KB Invariant conditions for phase portraits of quadratic systems with complex conjugate invariant lines meeting at a finite point / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques (France)) ; Vulpe, Nicolae (Vladimir Andrunakievichi Institute of Mathematics and Computer Science (Moldova))
The goal of this article is to give invariant necessary and sufficient conditions for a quadratic system, presented in whatever normal form, to have anyone of 17 out of the 20 phase portraits of the family of quadratic systems with two complex conjugate invariant lines intersecting at a finite real point. [...]
2020 - 10.1007/s12215-020-00541-2
Rendiconti del Circolo Matematico di Palermo, vol. 70 (July 2020) p. 923-945  
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26.
13 p, 667.0 KB Gradient systems of harmonic polynomials / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Oscar (Universidade Federal de Viçosa. Departamento de Matemática (Brazil))
We characterize all local phase-portraits of the finite and infinite singular points of the gradient systems defined by the real harmonic polynomials in two variables. We classify all the non-equivalent topological phase portraits of the gradient systems in the Poincaré disc defined by harmonic polynomials of degree less than five.
2020 - 10.1016/j.jde.2020.06.056
Journal of differential equations, Vol. 269, Issue 11 (November 2020) , p. 10073-10084  
Detailed record - Creative Commons
27.
20 p, 1.0 MB Phase portraits of Bernoulli quadratic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pereira, Weber F. (Universidade Estadual Paulista. Departamento de Matemática (Brasil)) ; Pessoa, Claudio (Universidade Estadual Paulista. Departamento de Matemática (Brasil))
In this paper we study a new class of quadratic polynomial differential systems. We classify all global phase portraits in the Poincaré disk of Bernoulli quadratic polynomial differential systems in R2.
2020
Electronic journal of differential equations, Vol. 2020, Issue 48 (2020) , p. 1-19
2 documents
Detailed record - Creative Commons
28.
32 p, 1.2 MB Z₂-equivariant linear type bi-center cubic polynomial Hamiltonian vector fields / Chen, Ting (Guangdong University of Finance and Economics. School of Statistics and Mathematics (China)) ; Li, Shimin (Guangdong University of Finance and Economics. School of Mathematics and Statistics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the global dynamical behavior of Z₂-equivariant cubic Hamiltonian vector fields with a linear type bi-center at (±1,0). By using a series of symbolic computation tools, we obtain all possible phase portraits of these Z₂-equivariant Hamiltonian systems.
2020 - 10.1016/j.jde.2019.12.020
Journal of differential equations, Vol. 269, Issue 1 (June 2020) , p. 832-861  
Detailed record - Creative Commons
29.
14 p, 412.2 KB Topological classification of polynomial complex differential equations with all the critical points of centre type / Álvarez Torres, María Jesús (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens, Rafel (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
In this paper we study the global phase portrait of complex polynomial differential equations of degree n of the form z˙ = f(z), having all their critical points of center type. We give the exact number of topologically different phase portraits on the Poincaré disk when n ≤ 6 and, in the remaining cases, an upper bound for this number which only depends on n.
2010 - 10.1080/10236190903232654
Journal of Difference Equations and Applications, Vol. 16, Issue 5-6 (May 2010) , p. 411-423  
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30.
37 p, 678.9 KB Z2-symmetric planar polynomial Hamiltonian systems of degree 3 with nilpotent centers / Dias, Fabio Scalco (Universidade Federal de Itajubá. Instituto de Matemática e Computação (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We provide the normal forms and the global phase portraits in the Poincaré disk of all Z2-symmetric planar polynomial Hamiltonian systems of degree 3 having a nilpotent center at the origin.
2019
Electronic journal of differential equations, Vol. 2019, Issue 82 (2019) , p. 1-29
2 documents
Detailed record - Creative Commons

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