Quadratic planar differential systems with algebraic limit cycles via quadratic plane Cremona maps

Alberich-Carramiñana, Maria; Ferragut, Antoni; Llibre, Jaume

doi:10.1016/j.aim.2021.107924

Cited by 6 publications

(3 citation statements)

References 8 publications

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“…Let P (x, y) and Q(x, y) be two real polynomials of degree 2. Then the differential system (1) ẋ = P (x, y), ẏ = Q(x, y), is called a planar quadratic polynomial differential system, or in what follows simply a quadratic system. As usual the dot denotes derivative with respect to an independent variable t, called the time.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

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Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

Llibre

2021

Expositiones Mathematicae

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Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

“…• algebraic limit cycles in quadratic systems [1,52,54,67,88,89,90,91,132,143,144,148,149,154,156,157,185,224,230],…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

Llibre

2021

Expositiones Mathematicae

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“…Alberich-Carramiñana et al [10] considered a theory for constructing geometric models of quadratic Cremona transformations of a plane and three-dimensional space, as applied to solving problems of applied geometry. The work of Martí n-Pastor [2] is devoted to proving a theorem that provides two-two-digit quadratic correspondences between points of combined fields.…”

Section: Theoretical Overviewmentioning

confidence: 99%

Development and Definition of Biquadratic Transformations Using Spheres and Two-Way Hyperboloids

Baidabekov¹,

Kemelbekova²,

Kussebayev³

et al. 2022

MMEP

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The insufficient use of quadratic transformations in applied geometry is explained by the fact that the methods of quadratic transformations are not developed much, although dozens of works by leading experts in applied geometry are devoted to the study of this problem, the development of graphic models, and their application in applied geometry. The research is devoted to the development of the theory of definition of biquadratic transformations of the plane. The essence of the proposed method for modeling biquadratic transformations of the plane, generated by a binary mapping of two surfaces of the second order, facilitation and solution of complex problems of applied geometries. And also, by means of graphical models of biquadratic transformations of the plane to facilitate the construction of curves of the second and fourfold orders. Considering a combination of non-linear surfaces of the second order, obtain subgroups of biquadratic transformations of the plane. The developed algorithm will make it possible to determine mathematical models of canonical biquadratic transformations of the plane, which is necessary for their practical application.

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Planar Quadratic Differential Systems with Invariants of the Form $$a x^2+b x y+c y^2+d x+e y+c_1 t$$

Llibre,

Salhi

2024

Bull. Iran. Math. Soc.

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Quadratic planar differential systems with algebraic limit cycles via quadratic plane Cremona maps

Cited by 6 publications

References 8 publications

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

Development and Definition of Biquadratic Transformations Using Spheres and Two-Way Hyperboloids

Planar Quadratic Differential Systems with Invariants of the Form $$a x^2+b x y+c y^2+d x+e y+c_1 t$$

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