  Isoscalar and isovector monopole oscillations that correspond to giant
resonances in spherical nuclei are described in the framework of time-dependent
relativistic mean-field theory. Time-dependent and self-consistent calculations
that reproduce experimental data on monopole resonances in 208Pb, show that the
motion of the collective coordinate is regular for isoscalar oscillations, and
that it becomes chaotic when initial conditions correspond to the isovector
mode. Regular collective dynamics coexists with chaotic oscillations on the
microscopic level. Time histories, Fourier spectra, state-space plots, Poincare
sections, autocorrelation functions, and Lyapunov exponents are used to
characterize the nonlinear system and to identify chaotic oscillations.
Analogous considerations apply to higher multipolarities.
