UAB Digital Repository of Documents 3 records found  Search took 0.02 seconds. 
1.
14 p, 331.7 KB Global phase portraits of quadratic systems with a complex ellipse as invariant algebraic curve / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)
In this paper we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 y^2 1=0 as invariant algebraic curve. [...]
2018 - 10.1007/s10114-017-5478-y
Acta Mathematica Sinica. English Series, Vol. 34, issue 5 (2018) , p. 801-811  
2.
13 p, 731.7 KB On the Darboux integrability of the Hindmarsh-Rose burster / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the Hindmarsh–Rose burster which can be described by the differential system x?=y?x3+bx2+I?z,y?=1?5x2?y,z?=?(s(x?x0)?z), where b, I, ?, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. [...]
2018 - 10.1007/s10114-017-5661-1
Acta Mathematica Sinica. English Series, Vol. 34, issue 6 (2018) , p. 947-958  
3.
15 p, 739.0 KB Liouvillian and analytic integrability of the quadratic vector fields having an invariant ellipse / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
We characterize the Liouvillian and analytic integrability of the quadratic polynomial vector fields in R2 having an invariant ellipse. More precisely, a quadratic system having an invariant ellipse can be written into the form ˙x = x2+y2−1+y(ax+by+c), ˙y = −x(ax+by+c), and the ellipse becomes x2+y2 = 1. [...]
2014 - 10.1007/s10114-014-2484-1
Acta Mathematica Sinica. English Series, Vol. 30 Núm. 3 (2014) , p. 453-466  

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