ABSTRACT
There is a rich mathematical history of fixed point theorems. Many of these fixed point theorems apply to a broad array of underlying state spaces. Probably, the two most celebrated fixed point theorems are the Brouwer fixed point theorem and the contraction mapping theorem. This chapter explores two different fixed point theorems for functions on R. The Brouwer fixed point theorem states that every continuous function from a closed ball of R. The implicit function theorem is the key tool in understanding basic bifurcation theory. The persistence of dynamics with respect to changes to a parameter is referred to as structural stability. The logistic function of population growth can easily be modified to incorporate terms that take harvesting into account.
