Parametric Center-Focus Problem for Abel Equation
نویسندگان
چکیده
منابع مشابه
The Center Problem for the Abel Equation, Compositions of Functions, and Moment Conditions
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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Two classical problems on plane polynomial vector fields, Hilbert’s 16th problem about the maximal number of limit cycles in such a system and Poincaré’s center-focus problem about conditions for all trajectories around a critical point to be closed, can be naturally reformulated for the Abel differential equation y′ = p(x)y + q(x)y. Recently, the center conditions for the Abel equation have be...
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An Abel di erential 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 any its solution y x with the initial value y a small enough Let p q be polynomials and let P R p Q R q P and Q satisfy Polynomial Composition condition if there exist polynomials P Q and W such that P x P W x Q x Q W x and W a W b The main result of this paper is that for a xed p...
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ژورنال
عنوان ژورنال: Qualitative Theory of Dynamical Systems
سال: 2014
ISSN: 1575-5460,1662-3592
DOI: 10.1007/s12346-014-0118-8