UAB Digital Repository of Documents 15 records found  1 - 10next  jump to record: Search took 0.02 seconds. 
1.
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  
2.
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  
3.
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  
4.
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  
5.
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  
6.
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  
7.
29 p, 2.3 MB On the number of invariant conics for the polynomial vector fields defined on quadrics / Bolaños Rivera, Yudi Marcela (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
The quadrics here considered are the nine real quadrics: parabolic cylinder, elliptic cylinder, hyperbolic cylinder, cone, hyperboloid of one sheet, hyperbolic paraboloid, elliptic paraboloid, ellipsoid and hyperboloid of two sheets. [...]
2013 - 10.1016/j.bulsci.2013.04.003
Bulletin des Sciences Mathematiques, Vol. 137 (2013) , p. 746-774  
8.
10 p, 662.0 KB On the polynomial differential systems having polynomial first integrals / García, Belen (Universidad de Oviedo. Departamento de Matemáticas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pérez del Río, Jesús Suárez (Universidad de Oviedo. Departamento de Matemáticas)
We consider the class of complex planar polynomial differential systems having a polynomial first integral. Inside this class the systems having minimal polynomial first integrals without critical remarkable values are the Hamiltonian ones. [...]
2012 - 10.1016/j.bulsci.2011.11.003
Bulletin des Sciences Mathematiques, Vol. 136 (2012) , p. 309-316  
9.
15 p, 373.2 KB First integrals of local analytic differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Walcher, Sebastian (RWTH Aachen(Germany). Lehrstuhl A fur Mathematik)
We investigate formal and analytic first integrals of local analytic ordinary differential equations near a stationary point. A natural approach is via the Poincaré-Dulac normal forms: If there exists a formal first integral for a system in normal form then it is also a first integral for the semisimple part of the linearization, which may be seen as "conserved" by the normal form. [...]
2012 - 10.1016/j.bulsci.2011.10.003
Bulletin des Sciences Mathematiques, Vol. 136 (2012) , p. 342-359  
10.
17 p, 416.2 KB Periodic orbits for perturbed non-autonomous differential equations / Coll, Bartomeu (Universitat de les Illes Balears. Departament de Matemàtiques i Informàtica) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Prohens, Rafel (Universitat de les Illes Balears. Departament de Matemàtiques i Informàtica)
2012 - 10.1016/j.bulsci.2012.03.001
Bulletin des Sciences Mathematiques, Vol. 136 (2012) , p. 803-819  

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