Monotonicity of kneading sequences in families of one -kink maps

Kneading theory is a tool used to understand the dynamics of a unimodal map on an interval. It can also be used to work with topological entropy, a measure of the complexity of a dynamical system. The kneading sequence of a unimodal map, f, is denoted by K( f). This dissertation studies the class of unimodal maps called one-kink maps. For a one-kink map f, the monotonicity of the function s K(sf) for s between 0 and 1 is investigated. Some one-kink maps will be identified for which the function s K(sf) is monotone, and some other one-kink maps will be identified with s K(sf) non-monotone.