Dynamical System of Scalar Field from 2-Dimension to 3-D and its
  Cosmological Implication
  We give the three-dimensional dynamical autonomous systems for most of the
popular scalar field dark energy models including (phantom) quintessence,
(phantom) tachyon, k-essence and general non-canonical scalar field models,
change the dynamical variables from variables $(x, y, \lambda)$ to observable
related variables $(w_{\phi}, \Omega_{\phi}, \lambda)$, and show the intimate
relationships between those scalar fields that the three-dimensional system of
k-essence can reduce to (phantom) tachyon, general non-canonical scalar field
can reduce to (phantom) quintessence and k-essence can also reduce to (phantom)
quintessence for some special cases. For the applications of the
three-dimensional dynamical systems, we investigate several special cases and
give the exactly dynamical solutions in detail. In the end of this paper, we
argue that, it is more convenient and also has more physical meaning to express
the differential equations of dynamical systems in $(w_{\phi}, \Omega_{\phi},
\lambda)$ instead of variables $(x, y, \lambda)$ and to investigate the
dynamical system in 3-Dimension instead of 2-Dimension. We also raise a
question about the possibility of the chaotic behavior in the spatially flat
single scalar field FRW cosmological models in the presence of ordinary matter.
