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\centerline{\bf Searching Local Periodic Families of ODEs}
\centerline{\bf in a Normal Form Method}

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\centerline{Victor F. Edneral}
\centerline{Institute for Nuclear Physics}
\centerline{Moscow State University}
\centerline{119899 Vorobievy Gory, Moscow, Russia}
\centerline{Email: edneral@theory.npi.msu.su}

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Resume: The  report  describes the  method  of  approximating local
periodic  families of autonomous systems of ODE  with polynomial
nonlinearity  in right sides by Fourier-power series. There  are
several examples of a treatment of systems second and forth order.

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