Center conditions III: Parametric and model center problems

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On the trigonometric moment problem (2011, background): “st there are transformations to the trigonometric Abel equation (1.1) (see [6]). In particular, a necessary and sucient condition in order for (1.1) to have a parametric center to rst order in (see [4]) is (1.2) Z 2ˇ 0 Pk(w)dQ(w) = 0; k= 0;1;2;::: where Pand Qare primitives of pand q. The trigonomet”
Solution of the polynomial moment problem (2007, background): “The polynomial moment problem was posed in the series of papers [2]-[5] in connection with the center problem for the Abel differential equation dy dz = p(z)y(2) + q(z)y(3) (2)”
A counterexample to the “composition conjecture" (2002, background): “In particular, the truth of the composition conjecture was established under the additional assumption that a;b are not critical points of P (z) (see [4]) and under some other additional assumptions (see [ 2 ], [3] and [5]).”