ON THE STRUCTURE OF THE KNEADING SPACE OF BIMODAL DEGREE ONE CIRCLE MAPS

Abstract

In this paper, we introduce an index space and two ⋆-like operators that can be used to describe bifurcations for parametrized families of degree one circle maps. Using these topological tools, we give a description of the kneading space, that is, the set of all dynamical combinatorial types for the class of all bimodal degree one circle maps considered as dynamical systems.