Dynamical properties of Euclidean solutions in a multidimensional cosmological model

In the framework of the Hartle-Hawking no-boundary proposal, we investigate d quantum creation of the multidimensional universe with a cosmological con stant (Lambda) but without matter fields. We have found that the classical solutions of the Euclidean Einstein equations in this model have "quasi-att ractors", i.e., most trajectories on the a-b plane, where a and b are the s cale factors of external and internal spaces, go around a point. It is pres umed that the wave function of the universe has a hump near this quasi-attr actor point. In the case that both the curvatures of external and internal spaces are positive, and Lambda > 0, there exist Lorentzian solutions which start near the quasi-attractor, the internal space remains microscopic, an d the external space evolves into our macroscopic universe.