Resultats globals: 10 registres trobats en 0.04 segons.
Articles, 10 registres trobats
Articles 10 registres trobats  
1.
9 p, 291.9 KB On the global dynamics of a finance model / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia
Recently several works have studied the following model of finance \[ x= z (y-a) x, y= 1-b y -x^2, z= -x -c z, \] where a, b and c are positive real parameters. We study the global dynamics of this polynomial differential system, and in particular for a one--dimensional parametric subfamily we show that there is an equilibrium point which is a global attractor.
2018 - 10.1016/j.chaos.2017.10.026
Chaos, Solitons and Fractals, Vol. 106 (2018) , p. 1-4  
2.
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)  
3.
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  
4.
21 p, 642.5 KB Phase portraits of quadratic Lotka-Volterra systems with a Darboux invariant in the Poincaré disc / Bolaños Rivera, Yudi Marcela (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We characterize the global phase portraits in the Poincaré disc of all the planar Lotka–Volterra quadratic polynomial differential systems having a Darboux invariant.
2014 - 10.1142/S0219199713500417
Communications in Contemporaray Mathematics, Vol. 16 Núm. 6 (2014) , p. 1350041 (23 pages)  
5.
11 p, 614.5 KB Darboux invariants for planar polynomial differential systems having an invariant conic / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Messias, Marcelo (FCT–UNESP(Brazil). Departamento de Matemática e Computacâo) ; Reinol, Alison C. (FCT–UNESP(Brazil). Departamento de Matemática e Computacâo)
We characterize all the planar polynomial differential systems with a unique invariant algebraic curve given by a real conic and having a Darboux invariant.
2014 - 10.1007/s00033-013-0390-5
ZAMP. Journal of Applied Mathematics and Physics, Vol. 65 (2014) , p. 1127-1136  
6.
11 p, 532.6 KB Morphisms and inverse problems for Darboux integrating factors / 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)
Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well-understood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane may remove degeneracies of the curve, and thus allow more structural insight. [...]
2013 - 10.1017/S0308210511001430
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, Vol. 143 Núm. 6 (2013) , p. 1291-1302  
7.
16 p, 625.7 KB Liouvillian first integrals of quadratic-linear polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Instituto Superior Técnico (Lisboa). Departamento de Matemática)
For a large class of quadratic–linear polynomial differential systems with a unique singular point at the origin having non-zero eigenvalues, we classify the ones which have a Liouvillian first integral, and we provide the explicit expression of them.
2011 - 10.1016/j.jmaa.2010.12.033
Journal of Mathematical Analysis and Applications, Vol. 379 (2011) , p. 188-199  
8.
7 p, 277.9 KB The integrability of the Nose-Hoover equation / Mahdi, Adam (University of North Carolina at Charlotte. Mathematics Department) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
In this work we consider the Nos´e–Hoover equation for a one dimensional oscillator x˙ = −y − xz, y˙ = x, z˙ = α(x2 − 1). It models the interaction of a particle with a heat–bath. We contribute to the understanding of its global dynamics, or more precisely, to the topological structure of its orbits by studying the integrability problem. [...]
2011 - 10.1016/j.geomphys.2011.02.018
Journal of Geometry and Physics, Vol. 61 (2011) , p. 1348-1352  
9.
17 p, 376.7 KB Quadratic systems with invariant straight lines of total multiplicity two having Darboux invariants / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene D. S. (Universidade de Sâo Paulo (Brazil). Departamento de Matemática)
In this paper we present the global phase portraits in the Poincaré disc of the planar quadratic polynomial systems which admit invariant straight lines with total multiplicity two and Darboux invariants.
2015 - 10.1142/S0219199714500187
Communications in Contemporaray Mathematics, Vol. 17 Núm. 3 (2015) , p. 1450018  
10.
21 p, 502.4 KB Normal Forms for Polynomial Differential Systems in R^3 Having an Invariant Quadric and a Darboux Invariant / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Messias, Marcelo (FCT–UNESP (Brazil). Departamento de Matemática e Computacâo) ; Reinol, Alison C. (FCT–UNESP (Brazil). Departamento de Matemática e Computacâo)
We give the normal forms of all polynomial differential systems in R^3 which have a nondegenerate or degenerate quadric as an invariant algebraic surface. We also characterize among these systems those which have a Darboux invariant constructed uniquely using the invariant quadric, giving explicitly their expressions. [...]
2015 - 10.1142/S0218127415500157
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 25 Núm. 1 (2015) , p. 1550015  

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