Inflation as a dynamical effect of higher dimensions

The possibility of explaining the inflationary phase of the evolution of the Universe as a dynamical effect of extra dimensions is discussed. Methods of qualitative dynamical systems have been applied to determine the regions of the phase space in which inflation takes place. The problem is analyzed within the class of multidimensional $\mathrm{F}\mathrm{r}\mathrm{i}\mathrm{e}\mathrm{d}\mathrm{m}\mathrm{a}\mathrm{n}\mathrm{n}-\mathrm{R}\mathrm{o}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{s}\mathrm{o}\mathrm{n}-\mathrm{W}\mathrm{a}\mathrm{l}\mathrm{k}\mathrm{e}\mathrm{r}\times T^D$ models with a hydrodynamical energy-momentum tensor, material fields satisfying the Freund-Rubin ansatz, and quantum effects arising from massless scalar fields at the low-temperature approximation. The stability of inflation is also demonstrated.