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13 p, 297.3 KB

Limit cycles bifurcating from a family of reversible quadratic centers via averaging theory / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Nabavi, Arefeh (Isfahan University of Technology. Department of Mathematical Sciences (Iran)) ; Mousavi, Marzieh (Isfahan University of Technology. Department of Mathematical Sciences (Iran))
Consider the class of reversible quadratic systems x· = y, y· = -x + x²+ y² - r², with r > 0. These quadratic polynomial differential systems have a center at the point ((1 -√(1+4r²)/2, 0) and the circle x² + y² = r² is one of the periodic orbits surrounding this center. [...]
2020 - DOI (Digital Object Identifier)

10.1142/S0218127420500510
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 30, Issue 4 (March 2020) , p. 2050051

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12 p, 664.4 KB

Formal Weierstrass nonintegrability criterion for some classes of polynomial differential systems in C² / Giné, Jaume (Universitat de Lleida. Departament de Matemàtica) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper, we present a criterion for determining the formal Weierstrass nonintegrability of some polynomial differential systems in the plane C². The criterion uses solutions of the form y = f(x) of the differential system in the plane and their associated cofactors, where f(x) is a formal power series. [...]
2020 - DOI (Digital Object Identifier)

10.1142/S0218127420500649
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 30, Issue 4 (March 2020) , art. 2050064

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