Patterns of bifurcation in iterated function systems

It was recently described [S. Bahar, Chaotic orbits and bifurcation from a fixed point generated by an iterated function system. Chaos, Solitons & Fractals, 5, 1001–1006 (1995), and S. Bahar, Further studies of bifurcations and chaotic orbits generated by iterated function systems. Chaos, Solitons & Fractals, 7, 41–47 (1996)] that bifurcation from a fixed point can occur in an iterated function system (IFS). This is unusual, since such bifurcation is usually observed in nonlinear rather than linear systems. Here, we investigate further the mechanisms by which such bifurcations occur.