This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and hyperplanes in projective space leads to c...

This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and hyperplanes in projective space leads to c...

An iterated function system on X R d is deened by successively iterating an i.i.d. sequence of random Lipschitz functions from X to X. This paper shows how Fn = f 1 fn may converge even in the absence of the strong contraction conditions | for instance, Lipschitz constant smaller than 1 on average | which earlier work has required. Instead, it is posited that there be a region of contraction wh...