Acta Mathematica Sinica English Series - Search Results - UAB Digital Repository of Documents

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10 p, 690.8 KB

Weierstrass integrability of complex differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We characterize the complex differential equations of the form dydx=an(x)yn+an−1(x)yn−1+⋯+a1(x)y+a0(x), where a(x) are meromorphic functions in the variable x for j = 0,…,n that admit either a Weierstrass first integral or a Weierstrass inverse integrating factor.
2021 - DOI (Digital Object Identifier)

10.1007/s10114-021-8374-4
Acta Mathematica Sinica. English Series, Vol. 37, Issue 10 (October 2021) , p. 1497-1506

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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 1973- (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 - DOI (Digital Object Identifier)

10.1007/s10114-017-5478-y
Acta Mathematica Sinica. English Series, Vol. 34, issue 5 (2018) , p. 801-811

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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 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the HindmarshRose 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 - DOI (Digital Object Identifier)

10.1007/s10114-017-5661-1
Acta Mathematica Sinica. English Series, Vol. 34, issue 6 (2018) , p. 947-958

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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 1973- (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 - DOI (Digital Object Identifier)

10.1007/s10114-014-2484-1
Acta Mathematica Sinica. English Series, Vol. 30 Núm. 3 (2014) , p. 453-466

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