Quantal Bifurcations in Rotational Spectra of Some Odd Atomic Nuclei

To show the existence of precursor phenomena of the transition order$\ to$chaos in atomic nuclei a simple analysis has been made, based on a recent criterion proposed by Pavli\-chenkov. The basic idea is that nonlinear effects in rotational bands should lead to bifurcation, which qualitatively changes the spectrum for one of the nuclear excitation branches. Experimental data concerning the isotopes of Er, Hf, Yb, Os, Dy, W strongly support the above criterion.