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 } ^ { \prime } for the thawing solutions .
If we use the observational constraint w _ { \phi 0 } < -0.8 and 0.2 < \Omega _ { m 0 } < 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 .