UAB Digital Repository of Documents 19 records found  1 - 10next  jump to record: Search took 0.02 seconds. 
1.
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  
2.
Global phase portraits of the generalized van der Pol systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We consider the generalized van der Pol systems x˙ = y, y˙ = −x + (1−x) f(y), where f ∈ R[y]. The classical van der Pol systems have f(y) = y. We first characterize when the origin of the generalized van der Pol systems is a center, and second we provide the global phase portraits in the Poincaré disc of the generalized van der Pol when f(y) = ay + ay for all a,a ∈ R.
2023 - 10.1016/j.bulsci.2022.103213
Bulletin des Sciences Mathematiques, Vol. 182 (February 2023) , art. 103213  
3.
Limit cycles of generic piecewise center-type vector fields in R3 separated by either one plane or by two parallel planes / Villanueva, Yovani (Universidade Federal de Goiâs. Instituto de Matemática e Estatística (Brazil)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Euzébio, R (Universidade Federal de Goiâs. Instituto de Matemática e Estatística (Brazil))
While the limit cycles of the piecewise differential systems in the plane R2 have been studied intensively during these last twenty years, this is not the case for the limit cycles of the piecewise differential systems in the space R3. [...]
2022 - 10.1016/j.bulsci.2022.103173
Bulletin des Sciences Mathematiques, Vol. 179 (October 2022) , art. 103173  
4.
9 p, 656.2 KB Limit cycles of piecewise differential equations on the cylinder / Bakhshalizadeh, Ali (Isfahan University of Technology. Department of Mathematical Sciences (Iran)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We consider the discontinuous piecewise differential equations of the form [Formula presented] where a0(t),a1(t),. . . ,an(t) and b0(t),b1(t),. . . ,bm(t) are 2π-periodic functions in the variable t, and we study the number of limit cycles of such equations on the cylinder. [...]
2021 - 10.1016/j.bulsci.2021.103013
Bulletin des Sciences Mathematiques, Vol. 170 (September 2021) , art. 103013  
5.
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  
6.
15 p, 671.3 KB Integrability and zero-Hopf bifurcation in the Sprott A system / Barreira, Luis (Universidade Técnica de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
The first objective of this paper is to study the Darboux integrability of the polynomial differential system x˙=y, y˙=−x−yz, z˙=y²−a and the second one is to show that for a > 0 sufficiently small this model exhibits one small amplitude periodic solution that bifurcates from the origin of coordinates when a = 0. [...]
2020 - 10.1016/j.bulsci.2020.102874
Bulletin des Sciences Mathematiques, Vol. 162 (September 2020) , art. 102874  
7.
8 p, 714.8 KB Rational first integrals in the Darboux theory of integrability in Cn / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics (China))
In 1976 Jouanolou showed that if the number of invariant algebraic hypersurfaces of a polynomial vector field in Rn or Cn of degree d is at least (d + n/n− 1) + n, then the vector field has a rational first integral. [...]
2010 - 10.1016/j.bulsci.2007.12.001
Bulletin des Sciences Mathematiques, Vol. 134, Issue 2 (March 2010) , p. 189-195  
8.
14 p, 337.6 KB Local Darboux first integrals of analytic differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Walcher, Sebastian (RWTH Aachen(Germany). Lehrstuhl A fur Mathematik) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)
In this paper we discuss local and formal Darboux first integrals of analytic differential systems, using the theory of Poincaré Dulac normal forms. We study the effect of local Darboux integrability on analytic normalization. [...]
2014 - 10.1016/j.bulsci.2013.09.007
Bulletin des Sciences Mathematiques, Vol. 138 (2014) , p. 71-88  
9.
15 p, 373.1 KB Simultaneous bifurcation of limit cycles from a linear center with extra singular points / Pérez-González, Set (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The period annuli of the planar vector field x' = −yF(x, y), y' = xF(x, y), where the set {F(x, y) = 0} consists of k different isolated points, is defined by k + 1 concentric annuli. In this paper we perturb it with polynomials of degree n and we study how many limit cycles bifurcate, up to a first order analysis, from all the period annuli simultaneously in terms of k and n. [...]
2014 - 10.1016/j.bulsci.2013.09.004
Bulletin des Sciences Mathematiques, Vol. 138 (2014) , p. 124-138  
10.
13 p, 727.8 KB Reduction of periodic difference systems to linear or autonomous ones / Li, Weigu (Peking University. School of Mathematical Sciences) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Wu, Hao (Peking University. School of Mathematical Sciences)
We extend Floquet theory for reducing nonlinear periodic difference systems to autonomous ones (actually linear) by using normal form theory.
2013 - 10.1016/j.bulsci.2011.01.001
Bulletin des Sciences Mathematiques, Vol. 137 (2013) , p. 129-139  

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