The Center Problem for the Abel Equation, Compositions of Functions, and Moment Conditions
نویسندگان
چکیده
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 of P = ∫ p and Q = ∫ q on the one hand and to vanishing conditions for the moments mi,j = ∫ P Qq on the other hand. We give a detailed review of the recent results in each of these directions. 2000 Math. Subj. Class. Primary: 30E99, 30C99; Secondary: 34C99.
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