Inducing fixed points in the Stone-Cech compactification

If f is an autohomeomorphism of some space X, then beta f denotes its Stone-Cech extension to beta X. For each n less than or equal to omega, we give an example of a first countable, strongly zero-dimensional, subparacompact X and a map f such that every point of X has an orbit of size n under f and beta f has a fixed point. We give an example of a normal, zero-dimensional X such that f is fixed-point-free but beta f is not. We note that it is impossible for every point of X to have an orbit of size 3 and beta X to have a point with orbit of size 2.