We show how to extend the methods of resurgent analysis from the usual trans-serial objects: formal Fatou coordinates of parabolic diffeomorphisms of (C,0), to some dynamical objects: orbits of said diffeomorphisms. In the situation when the orbit is real, we also show how to apply such analysis to the associated fractal-theoretic objects: tube function and counting function of the orbit. This is a joint work with Pavao Mardesic, Goran Radunovic and Maja Resman.