  Tracking quintessence, in a spatially flat and isotropic space-time with a
minimally coupled canonical scalar field and an asymptotically inverse
power-law potential $V(\varphi)\propto\varphi^{-p}$, $p>0$, as
$\varphi\rightarrow0$, is investigated. This is done by introducing a new
three-dimensional \emph{regular} dynamical system, which enables a rigorous
explanation of the tracking feature: 1) The dynamical system has a tracker
fixed point $\mathrm{T}$ with a two-dimensional stable manifold that pushes an
open set of nearby solutions toward a single tracker solution originating from
$\mathrm{T}$. 2) All solutions, including the tracker solution and the
solutions that track/shadow it, end at a common future attractor fixed point
that depends on the potential. Thus, the open set of solutions that shadow the
tracker solution share its properties during the tracking quintessence epoch.
We also discuss similarities and differences of underlying mechanisms for
tracking, thawing and scaling freezing quintessence, and, moreover, we
illustrate with state space pictures that all of these types of quintessence
exist simultaneously for certain potentials.
