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Articles, 24 registres trobats
Articles 24 registres trobats  1 - 10següentfinal  anar al registre:
1.
17 p, 752.4 KB Classical Planar Algebraic Curves Realizable by Quadratic Polynomial Differential Systems / García, Isaac A. (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we show examples of planar quadratic differential systems having some famous planar invariant algebraic curves. We carry out a non exhaustive classification taking into account the degree of the invariant algebraic curve. [...]
2017 - 10.1142/S0218127417501413
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 27 Núm. 9 (2017) , p. 1750141 (12 pages)  
2.
14 p, 708.3 KB On the integrability of the 5-dimensional Lorenz system for the gravity-wave activity / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We consider the 5-dimensional Lorenz system \[ U' &= -V W b V Z, \\ V' &= UW-b UZ, \\ W'&= -U V,\\ X' &= -Z, \\ Z'&=b UV X \] where b \R \0\ and the derivative is with respect to T. [...]
2017
Proceedings of the American Mathematical Society, Vol. 145 Núm. 2 (2017) , p. 665-679  
3.
22 p, 505.3 KB Dynamics, integrability and topology for Lotka-Volterra Hamiltonian systems in R^4 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Xiao, Dongmei (Shanghai Jiao Tong University. School of Mathematical Sciences)
In this paper first we give the sufficient and necessary conditions in order that two classes of polynomial Kolmogorov systems in \R_ ^4 are Hamiltonian systems. After we study the integrability of these Hamiltonian systems in the Liouville sense. [...]
2017 - 10.1016/j.jde.2016.10.042
Journal of Differential Equations, Vol. 262 Núm. 3 (2017) , p. 2231-2253  
4.
15 p, 651.1 KB Centers of weight-homogeneous polynomial vector fields on the plane / Giné, Jaume (Universitat de Lleida. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
We characterize all centers of a planar weight-homogeneous polynomial vector fields. Moreover we classify all centers of a planar weight-homogeneous polynomial vector fields of degrees 6 and 7.
2017
Proceedings of the American Mathematical Society, Vol. 145 Núm. 6 (2017) , p. 2539-2555  
5.
14 p, 310.6 KB On the dynamics of a model with coexistence of three attractors: a point, a periodic orbit and a strange attractor / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
For a dynamical system described by a set of autonomous differential equations, an attractor can be either a point, or a periodic orbit, or even a strange attractor. Recently a new chaotic system with only one parameter has been presented where besides a point attractor and a chaotic attractor, it also has a coexisting attractor limit cycle which makes evident the complexity of such a system. [...]
2017 - 10.1007/s11040-017-9240-6
Mathematical Physics, Analysis and Geometry. An International Journal Devoted to the Theory and Applications of Analysis and Geometry to Physics, Vol. 20 Núm. 2 (2017) , p. 1-12  
6.
16 p, 266.5 KB On the complete integrability of the Raychaudhuri differential system in R^4 and of a CRNT model in R^5 / Ferragut, Antoni (Universitat Jaume I. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
WestudytheDarbouxintegrabilityoftwodifferentialsystemswithparam- eters: the Raychaudhuri equation (a relativistic model in R4) and a chemical reaction model in R5. We prove that the first one is completely integrable and that the first inte- grals are of Darboux type. [...]
2017 - 10.1007/s12346-017-0230-7
Qualitative Theory of Dynamical Systems, 2017  
7.
13 p, 292.9 KB On the Darboux integrability of a cubic CRNT model in R^5 / Ferragut, Antoni (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the Darboux integrability of a differential system with parameters coming from a chemical reaction model in R5. We find all its Darboux polynomials and exponential factors and we prove that it is not Darboux integrable.
2016 - 10.1016/j.chaos.2015.11.011
Chaos, Solitons and Fractals, Vol. 82 (2016) , p. 131-138  
8.
32 p, 789.9 KB The 16th Hilbert problem restricted to circular algebraic limit cycles / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d’Enginyeria Informàtica i Matemàtiques) ; Ramírez, Valentín (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II) ; Sadovskaia, Natalia (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II)
We prove the following two results. First every planar polynomial vector field of degree S with S invariant circles is Darboux integrable without limit cycles. Second a planar polynomial vector field of degree S admits at most S - 1 invariant circles which are algebraic limit cycles. [...]
2016 - 10.1016/j.jde.2015.12.019 0022-0396
Journal of Differential Equations, Vol. 260 (2016) , p. 5726-5760  
9.
13 p, 810.8 KB Liouvillian integrability versus Darboux polynomials / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática) ; Zhang, Xiang (Shanghai Jiao Tong University. Department of Mathematics)
In this note we provide a sufficient condition on the existence of Darboux polynomials of polynomial differential systems via existence of Jacobian multiplier or of Liouvillian first integral and a degree condition among different components of the system. [...]
2016 - 10.1007/s12346-016-0212-1
Qualitative Theory of Dynamical Systems, Vol. 15 (2016) , p. 503-515  
10.
14 p, 706.0 KB Darboux integrability of 2-dimensional Halmiltonian systems with homogeneous potentials of degree 3 / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We provide a characterization of all Hamiltonian systems of the form H = (p21 + p22)/2 + V (q1, q2) where V is a homogenous polynomial of degree 3 which are completely integrable with Darboux first integrals.
2014 - 10.1063/1.4868701
Journal of Mathematical Physics, Vol. 55 (2014) , p. 33507  

Articles : 24 registres trobats   1 - 10següentfinal  anar al registre:
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