  In recent years, the so-called polynomial moment problem, motivated by the
classical Poincare center-focus problem, was thoroughly studied, and the
answers to the main questions have been found. The study of a similar problem
for rational functions is still at its very beginning. In this paper, we make
certain progress in this direction; namely, we construct an example of a
Laurent polynomial for which the solutions of the corresponding moment problem
behave in a significantly more complicated way than it would be possible for a
polynomial.
