Abstract:

During this talk, we will consider several examples of how externalrays in the dynamical plane may be extended completely through theJulia sets of certain rational maps. These are maps of the form $zn+C\; /\; zn$. In this case most of these extended rays are simple closedcurves passing through the origin (a pole) and infinity. They also cutacross the Julia set in a Cantor set of points. In certain cases,these extended rays meet a critical orbit, in which case theybifurcate into simple closed curves with (possibly infinitely many)attached arcs. This is joint work with Bob Devaney and Figen Cilinger.