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We establish a polynomial normal form for a vector field having a limit cycle of multiplicity 2. The smooth classification problem for such fields is closely related to the problem of classification of germs $\Delta :({ℝ}^1,0)\to ({ℝ}^1,0)$, $\Delta \left(x\right)=x+c{x}^2+\cdots$, solved by F. Takens in 1973. Such germs appear as the germs of Poincaré return maps for semistable cycles, and a smooth conjugacy between any two such germs may be extended to a smooth orbital equivalence between the original fields. If one deals with smooth conjugacy of flows...