Results overview: Found 7 records in 0.04 seconds.
Articles, 7 records found
Articles 7 records found  
1.
15 p, 434.9 KB New Family of Centers of Planar Polynomial Differential Systems of Arbitrary Even Degree / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mousavi, Marzieh (Isfahan University of Technology. Department of Mathematical Sciences) ; Nabavi, Arefeh (Isfahan University of Technology. Department of Mathematical Sciences)
The problem of distinguishing between a focus and a center is one of the classical problems in the qualitative theory of planar differential systems. In this paper, we provide a new family of centers of polynomial differential systems of arbitrary even degree. [...]
2019 - 10.1007/s10883-019-09432-x
Journal of Dynamical and Control Systems, Vol. 25, issue 4 (Oct. 2019) , p. 619-630  
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.
7 p, 568.5 KB Cofactors and equilibria for polynomial vector fields / Ferragut, Antoni (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We provide a relationship between the existence of equilibrium points of differential systems and the cofactors of invariant algebraic curves and exponential factors of the system.
2014 - 10.1017/S0308210513000425
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, Vol. 144A (2014) , p. 753-760  
4.
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  
5.
7 p, 591.8 KB A note on Liouvillian first integrals and invariant algebraic curves / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Grau, Maite (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the existence and non-existence of finite invariant algebraic curves for complex planar polynomial differential system having a Liouvillian first integral.
2013 - 10.1016/j.aml.2012.09.008
Applied mathematics letters, Vol. 26 (2013) , p. 285-289  
6.
20 p, 347.7 KB Planar vector fields with a given set of orbits / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Sadovskaia, Natalia (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II)
We determine all the C 1 planar vector fields with a given set of orbits of the form y − y(x) = 0 satisfying convenient assumptions. The case when these orbits are branches of an algebraic curve is also study. [...]
2011 - 10.1007/s10884-011-9219-0
Journal of dynamics and differential equations, Vol. 23 Núm. 4 (2011) , p. 885-902  
7.
28 p, 497.5 KB A class of polynomial planar vector fields with polynomial first integral / Ferragut, Antoni (Universitat Jaume I. IMAC i Departament de Matemàtiques) ; Galindo, Carlos (Universitat Jaume I. IMAC i Departament de Matemàtiques) ; Monserrat, Francisco (Universitat Politècnica de València. E.T.S. d'Informatica Aplicada)
2015 - 10.1016/j.jmaa.2015.04.062
Journal of mathematical analysis and applications, Vol. 430 (2015) , p. 354-380  

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