  We study in detail the motions of three planets interacting with each other
under the influence of a central star. It is known that the system with more
than two planets becomes unstable after remaining quasi-stable for long times,
leading to highly eccentric orbital motions or ejections of some of the
planets. In this paper, we are concerned with the underlying physics for this
quasi-stability as well as the subsequent instability and advocate the
so-called "stagnant motion" in the phase space, which has been explored in the
field of dynamical system. We employ the Lyapunov exponent, the power spectra
of orbital elements and the distribution of the durations of quasi-stable
motions to analyze the phase space structure of the three-planet system, the
simplest and hopefully representative one that shows the instability. We find
from the Lyapunov exponent that the system is almost non-chaotic in the initial
quasi-stable state whereas it becomes intermittently chaotic thereafter. The
non-chaotic motions produce the horizontal dense band in the action-angle plot
whereas the voids correspond to the chaotic motions. We obtain power laws for
the power spectra of orbital eccentricities. Power-law distributions are also
found for the durations of quasi-stable states. All these results combined
together, we may reach the following picture: the phase space consists of the
so-called KAM tori surrounded by satellite tori and imbedded in the chaotic
sea. The satellite tori have a self-similar distribution and are responsible
for the scale-free power-law distributions of the duration times. The system is
trapped around one of the KAM torus and the satellites for a long time (the
stagnant motion) and moves to another KAM torus with its own satellites from
time to time, corresponding to the intermittent chaotic behaviors.
