Weak and strong composition conditions for the Abel differential equation
نویسندگان
چکیده
منابع مشابه
Center and Composition Conditions for Abel Differential Equation, and Rational Curves
We consider the Abel Equation ρ′ = p(θ)ρ2 + q(θ)ρ3 (*) with p(θ), q(θ) polynomials in sin θ, cos θ. The center problem for this equation (which is closely related to the classical center problem for polynomial vector fields on the plane) is to find conditions on p and q under which all the solutions ρ(θ) of this equation are periodic, i.e. ρ(0) = ρ(2π) for all initial values ρ(0). We consider t...
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An Abel differential equation y′ = p(x)y + q(x)y is said to have a center at a pair of complex numbers (a, b) if y(a) = y(b) for every solution y(x) with the initial value y(a) small enough. This notion is closely related to the classical center-focus problem for plane vector fields. Recently, conditions for the Abel equation to have a center have been related to the composition factorization o...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 2014
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2014.06.001