The general property of dynamical quintessence field
  We discuss the general dynamical behaviors of quintessence field, in
particular, the general conditions for tracking and thawing solutions are
discussed. We explain what the tracking solutions mean and in what sense the
results depend on the initial conditions. Based on the definition of tracking
solution, we give a simple explanation on the existence of a general relation
between $w_\phi$ and $\Omega_\phi$ which is independent of the initial
conditions for the tracking solution. A more general tracker theorem which
requires large initial values of the roll parameter is then proposed. To get
thawing solutions, the initial value of the roll parameter needs to be small.
The power-law and pseudo-Nambu Goldstone boson potentials are used to discuss
the tracking and thawing solutions. A more general $w_\phi-\Omega_\phi$
relation is derived for the thawing solutions. Based on the asymptotical
behavior of the $w_\phi-\Omega_\phi$ relation, the flow parameter is used to
give an upper limit on $w_\phi'$ for the thawing solutions. If we use the
observational constraint $w_{\phi 0}<-0.8$ and $0.2<\Omega_{m0}<0.4$, then we
require $n\lesssim 1$ for the inverse power-law potential
$V(\phi)=V_0(\phi/m_{pl})^{-n}$ with tracking solutions and the initial value
of the roll parameter $|\lambda_i|<1.3$ for the potentials with the thawing
solutions.
