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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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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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Universal centers in the cubic trigonometric Abel equation [PDF]
, 2014 We study the center problem for the trigonometric Abel equation $d \rho/ d \theta= a_1 (\theta) \rho^2 + a_2(\theta) \rho^3,$ where $a_1(\theta)$ and $a_2(\theta)$ are cubic trigonometric polynomials in $\theta$.
Giné, Jaume +2 more
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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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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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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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Nondegenerate centers for Abel polynomial differential equations of second kind [PDF]
, 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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A simple solution of some composition conjectures for Abel equations [PDF]
, 2013 El títol de la versió pre-print de l'article és: The solution of the composition conjecture for Abel equationsTrigonometric Abel differential equations appear when one studies the number of limit cycles and the center-focus problem for certain families ...
Cimà, Anna +2 more
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