We study the center problem for the trigonometric Abel equation $d ho/ d heta= a_1 (heta) ho^2 + a_2(heta) ho^3,$ where $a_1(heta)$ and $a_2(heta)$ are cubic trigonometric polynomials in $heta$. This problem is closely connected with the classical Poincaré center problem for planar polynomial vector fields. A particular class of centers, the so-called universal centers or composition centers, is taken into account. An example of non-universal center and a characterization of all the universal centers for such equation are provided.
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