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Rational solutions and limit cycles of polynomial and trigonometric Abel equations
Electronic Journal of Qualitative Theory of Differential Equationse study the Abel differential equation $x'=A(t)x^3+B(t)x^2+C(t)x$. Specifically, we find bounds on the number of its rational solutions when $A(t), B(t)$ and $C(t)$ are polynomials with real or complex coefficients; and on the number of rational limit ...
Luis Ángel Calderón
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Homogeneous-Like Generalized Cubic Systems
International Journal of Differential Equations, 2016 We consider properties and center conditions for plane polynomial systems of the forms x˙=-y-p1(x,y)-p2(x,y), y˙=x+q1(x,y)+q2(x,y) where p1, q1 and p2, q2 are polynomials of degrees n and 2n-1, respectively, for integers n≥2. We restrict our attention to
G. R. Nicklason
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Electronic Journal of Differential Equations, 2017 Let $A(\theta)$ non-constant and $B_j(\theta)$ for $j=0,1,2,3$ be real trigonometric polynomials of degree at most $\eta \ge 1$ in the variable x. Then the real equivariant trigonometric polynomial Abel differential equations $A(\theta) y' =B_1(\theta)
Claudia Valls
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Nondegenerate centers for Abel polynomial differential equations of second kind [PDF]
Journal of Computational and Applied Mathematics, 2017 In this paper we study the center problem for Abel polynomial differential equations of second kind. Computing the focal values and using modular arithmetics and Gröbner bases we find the center conditions for such systems for lower degrees.The first ...
Giné, Jaume, Valls, Claudia
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Manufacturing a mathematical group: a study in heuristics [PDF]
, 2018 I examine the way a relevant conceptual novelty in mathematics, that is, the notion of group, has been constructed in order to show the kinds of heuristic reasoning that enabled its manufacturing.
Ippoliti, Emiliano
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Singular Phases of Seiberg-Witten Integrable Systems: Weak and Strong Coupling [PDF]
, 2000 We consider the singular phases of the smooth finite-gap integrable systems arising in the context of Seiberg-Witten theory. These degenerate limits correspond to the weak and strong coupling regimes of SUSY gauge theories.
Braden, H. W., Marshakov, A.
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Seiberg-Witten Curves and Integrable Systems [PDF]
, 1999 This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of Seiberg-Witten curves ...
Marshakov, A.
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Superintegrable St\"ackel Systems on the Plane: Elliptic and Parabolic Coordinates [PDF]
, 2012 Recently we proposed a generic construction of the additional integrals of motion for the St\"ackel systems applying addition theorems to the angle variables.
Tsiganov, Andrey V.
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Uniqueness of limit cycles for quadratic vector fields [PDF]
, 2019 Producción CientíficaThis article deals with the study of the number of limit cycles surrounding a critical point of a quadratic planar vector field, which, in normal form, can be written as x ′ = a1x − y − a3x 2 + (2a2 + a5)xy+a6y 2 , y ′ = x ...
Bravo, José Luis +3 more
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Integrable Abel equations and Vein's Abel equation [PDF]
, 2016 We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein's Abel equation whose solutions are expressed in terms of the third order hyperbolic ...
Mancas, Stefan C., Rosu, Haret C
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