  We have presented a complete description of classical dynamics generated by
the Hamiltonian of quadrupole nuclear oscillations and identified those
peculiarities of quantum dynamics that can be interpreted as quantum
manifestations of classical stochasticity. Particular attention has been given
to investigation of classical dynamics in the potential energy surface with a
few local minima. A new technique is suggested for determination of the
critical energy of the transition to chaos. It is simpler than criteria of
transition to chaos connected with one or another version of overlap resonances
criterion. We have numerically demonstrated that for potential with a localized
unstable region motion becomes regular at the high energy again, i.e.
transition regularity-chaos-regularity {R - C - R} takes place for these
potentials. The variations of statistical properties of energy spectrum in the
process of {R - C - R) transition have been studied in detail. We proved that
the type of the classical motion is correlated with the structure of the
eigenfunctions of highly excited states in the (R - C - R) transition. Shell
structure destruction induced by the increase of nonintegrable perturbation was
analyzed.
