First, for the family P_{n,c}(z) = z^n + c, we show that the geometric limit
of the Mandelbrot sets M_n(P) as n tends to infinity exists and is the closed
unit disk, and that the geometric limit of the Julia sets J(P_{n,c}) as n tends
to infinity is the unit circle, at least when the modulus of c is not one. Then
we establish similar results for some generalizations of this family; namely,
the maps F_{t,c} (z) = z^t+c for real t>= 2, and the rational maps R_{n,c,a}
(z) = z^n + c + a/z^n.Comment: 29 pages, 16 figures (34 pic files), submitte