identical to those in Figure \[fig: orbit\_linear\]; however, in this set of images, the stars are in motion due to change in their angular momenta in the non-linear phase of orbital evolution (see also the supplementary video). When the stars are captured by the density enhancement ($T_{\rm rot} \simeq 11.8-12.0$), they radially migrate along the spiral arms. The stars approaching from behind the spiral arm (i.e., inner radius) tend to attain increased angular momenta via acceleration along the spiral arm, whereby they move to the disk’s outer radius. In contrast, the stars approaching ahead of the spiral arm (i.e., outer radius) tend to lose their angular momenta via deceleration along the spiral arm, and they move to the disk’s inner radius. Along the $\phi-L_{z}$ plane, the stars oscillate both horizontally as well as vertically. Moreover, the guiding centers of the oscillations do not remain constant at the same value of $L_{z}$. This is essentially different from the epicycle motion in which $L_{z}$ is conserved.

The Lindblad diagram in Figure \[fig:EvolutionSpiral\] shows that the stars oscillate along the curve of circular motion by undergoing change in terms of both angular momentum and energy. The oscillating stars successively undergo aggregation and disaggregation 