  We consider generalized closest return times of a complex polynomial of
degree at least two. Most previous studies on this subject have focused on the
properties of polynomials with particular return times, especially the
Fibonacci numbers. We study the general form of these closest return times. The
main result of this paper is that these closest return times are meta-Fibonacci
numbers. This result applies to the return times of a principal nest of a
polynomial. Furthermore, we show that an analogous result holds in a tree with
dynamics that is associated with a polynomial.
