Cylinders, multi-cylinders and the induced action of Aut(Fn)

Abstract

Abstract. A cylinder is the set of infinite words with fixed prefix u. A double-cylinder is “the same” for bi-infinite words. We show that for every word u and any automorphism of the free group F the image is a finite union of cylinders. The analogous statement is true for double cylinders. We give (a) an algorithm, and (b) a precise formula which allows one to determine this finite union of cylinders.