Study of the process $e^+e^- \to \pi^+\pi^-\pi^0$ in the energy region $\sqrt[]{s}$ from 0.98 to 1.38 GeV.}

The cross section of the process $e^+e^-\to \pi^+\pi^-\pi^0$ was measured in the Spherical Neutral Detector experiment at the VEPP-2M collider in the energy region $\sqrt[]{s} = 980 \div 1380$ MeV. The measured cross section, together with the $e^+e^-\to \pi^+\pi^-\pi^0$ and $\omega\pi^+\pi^-$ cross sections obtained in other experiments, was analyzed in the framework of the generalized vector meson dominance model. It was found that the experimental data can be described by a sum of $\omega$, $\phi$ mesons and two $\omega^\prime$ and $\omega^{\prime\prime}$ resonances contributions, with masses $m_{\omega^\prime}\sim 1490$,$m_{\omega^{\prime\prime}}\sim 1790$ MeV and widths $\Gamma_{\omega^\prime}\sim 1210$, $\Gamma_{\omega^{\prime\prime}}\sim 560$ MeV. The analysis of the $\pi^+\pi^-$ invariant mass spectra in the energy region $\sqrt[]{s}$ from 1100 to 1380 MeV has shown that for their descriptionone should take into account the $e^+e^-\to\omega\pi^0\to\pi^+\pi^-\pi^0$ mechanism also. The phase between the amplitudes corresponding to the $e^+e^-\to\omega\pi$ and $e^+e^-\to\rho\pi$ intermediate states was measured for the first time. The value of the phase is close to zero and depends on energy.