The dynamics and an index for real projective iterated function systems

I will give a reasonably complete description of the dynamics associated with arbitrary real projective iterated function systems, including their Conley decomposition (which describes the attractor/repeller structure), and a beautiful duality result. Using these ideas, a full "Conley landscape" can be "painted" for arbitrary real projective systems. One consequence is the existence of a new mathematical projective invariant: does it have physical significance? (This talk describes largely joint work with Andrew Vince and David Wilson of the University of Florida.)