Fractal basins of escape and the formation of spiral arms in a galactic potential with a bar

We investigate the dynamics in the close vicinity of and within the critical area in a 2D effective galactic potential with a bar of Zotos. We have calculated Poincar\'e surfaces of section and the basins of escape. In both the Poincar\'e surfaces of section and the basins of escape we find numerical evidence for the existence of a separatrix which hinders orbits from escaping out of the bar region. We present numerical evidence for the similarity between spiral arms of barred spiral galaxies and tidal tails of star clusters.