Julia sets of skew products for class MAp

Let f
j
∊M (j = 1,2,…, m; m≥1 and
$\tilde{f}$
be the skew product associated with the generator system
$\{f_{1}, f_{2}, \ldots, f_{m}\}
. Then
$F(\tilde{f})$
is completely invariant under
$(\tilde{f});J(\tilde{f})$
is completely invariant under
$\tilde{f}; J(\tilde{f})$
is perfect;
$J(\tilde{f})$
has interior points if and only if
$F(\tilde{f})=\oslash$
; if f
j
∊ MA
p
(p ≥ 5), j = 1, 2, …, m, then the set of the repelling fixed points of
$\tilde{f}$
of all orders are dense in
$J(\tilde{f})$
.