An embedding of the Farey web in the parameter space of simple families of circle maps

Abstract

An embedding of the Farey web, which is an extension of Farey tree, is described in the parameter space of simple circle maps. The effects of the embedding on the organization of frequency-locking and topological properties of the boundary between simple and complicated dynamics are discussed. A smooth Farey web is constructed and the results are stated in terms of the standard sine family.