On first return path systems

R. J. O'Malley introduced a new type of path system which he calls first return path system. Even though these paths are thin, they possess intersection property. In this paper by imposing different metrics on the space of sequences, we study the effect of turbulence on first return path systems. An example of a path system having intersection property, yet not containing any first return path system is given. We also present some condition under which a congruent path system can not contain a first return path system.