  This paper studies a version of counting problem in dynamical system that is
of interest specially in conformal dynamical systems where functions of the
systems are angle preserving. Recently M. Pollicott and M. Urba\'{n}ski
published a result in this context for D-generic systems where the complex
transfer operator behaves nice on the critical line of the Poincare series.
Their result contains an asymptotic formula for the planer Apollonian circle
packing. We lift the D-generic condition in the paper to see how their
asymptotic formula changes. Further we observed an asymptotic of length closely
related to this counting problem.
