A farey tree organization of locking regions for simple circle maps

Let f e a C3 circle endomorphism of degree one with exactly two critical points and negative Schwarzian derivative. Assume that there is no real number a such that f + a has a unique rotation number equal to p/q. Then the same holds true for any p′/q′ such that p/q stands above p′/q′ in the Farey tree and can be related to it by a path on the tree. © 1996 American Mathematical Society.