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Articles, 5 records found
Articles 5 records found  
1.
21 p, 834.1 KB Centers for generalized quintic polynominal differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matematica)
2017 - 10.1216/RMJ-2017-47-4-1097
The Rocky Mountain Journal of Mathematics, Vol. 47 Núm. 4 (2017) , p. 1097-1120  
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2.
18 p, 330.6 KB Global behaviour of the period function for some degenerate centers / Álvarez, Maria 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)
We study the global behaviour of the period function on the period annulus of degenerate centers for two families of planar polynomial vector fields. These families are the quasi-homogeneous vector fields and the vector fields given by the sum of two quasi-homogeneous Hamiltonian ones. [...]
2017 - 10.1016/j.jmaa.2016.12.077
Journal of mathematical analysis and applications, Vol. 449 Núm. 2 (2017) , p. 1553-1569  
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3.
14 p, 580.6 KB A method for characterizing nilpotent centers / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
To characterize when a nilpotent singular point of an analytic differential system is a center is of particular interest, first for the problem of distinguishing between a focus and a center, and after for studying the bifurcation of limit cycles from it or from its period annulus. [...]
2014 - 10.1016/j.jmaa.2013.12.013
Journal of mathematical analysis and applications, Vol. 413 (2014) , p. 537-545  
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4.
21 p, 834.7 KB Centers for a class of generalized quintic polynomial differential systems / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We classify the centers of the polynomial differential systems in R2 of degree d ≥ 5 odd that in complex notation writes as z˙ = iz + (zz¯)d−5/2 (Az5 + Bz4z¯ + Cz3z¯2 + Dz2z¯3 + Ezz¯4 + Fz¯5), where A, B, C, D, E, F ∈ C and either A = Re(D) = 0, or A = Im(D) = 0, or Re(A) = D = 0, or Im(A) = D = 0.
2014 - 10.1016/j.amc.2014.05.047
Applied Mathematics and Computation, Vol. 242 (2014) , p. 187-195  
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5.
18 p, 589.4 KB On the center conditions for analytic monodromic degenerate singularities / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we present two methods for detecting centers of monodromic degenerate singularities of planar analytic vector fields. These methods use auxiliary symmetric vector fields can be applied independently that the singularity is algebraic solvable or not, or has characteristic directions or not. [...]
2012 - 10.1142/S0218127412503038
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 22 Núm. 2 (2012) , p. 1250303 (11 pp.)  
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