  In the paper we investigate the behavior of trajectory of rational $p$-adic
dynamical system in complex $p$-adic filed $\C_p$. It is studied Siegel disks
and attractors of such dynamical systems. We show that Siegel disks may either
coincide or disjoin for different fixed points of the dynamical system.
Besides, we find the basin of the attractor of the system. It is proved that
such kind of dynamical system is not ergodic on a unit sphere with respect to
the Haar measure.
