  We investigate the spacetime properties of BTZ black holes in the presence of
the Maxwell field and Born-Infeld field and find rich properties in the
spacetime structures when the model parameters are varied. Employing the
Landau-Lifshitz theory, we examine the thermodynamical phase transition in the
charged BTZ black holes. We further study the dynamical perturbation in the
background of the charged BTZ black holes and find different properties in the
dynamics when the thermodynamical phase transition occurs.
