Published online by Cambridge University Press: 19 September 2008
The main results of this paper are the following theorem and its corollary.
Theorem 0.1. Suppose that f: S2 → S2 is an orientation-preserving homeomorphism of the two-dimensional sphere and that Fix (f) is a finite set containing at least three points. If f has a dense orbit then the number of periodic points of period n for some iterate of f grows exponentially in n.