Abstract: Let Wbe an
invariant nonrecurrent Fatou component associated with the automorphism Assume that all of the limit maps
of are constant. We prove the
following theorem. If there is more than one such limit map, then there are
uncountably many. The images of these limit maps form a closed set in the
boundary of W
containing no isolated points. Additionally, there cannot be more than one limit
map unless the derivative of F along a
specific subset of the curve of fixed points of F has eigenvalues 1 and with q
non-Diophantine.
Keywords and phrases: Fatou component, nonrecurrent, invariant.
