Hubbard trees and their properties.

A Hubbard tree is a set of points at the core of dendritic Julia sets. These trees encapsulate all the information about the larger Julia set, but in a much smaller, easier to understand structure. We discuss the structure of Hubbard trees, in particular, we provide a useful definition of branch point and endpoint. Afterwards, we demonstrate the existence of some trees that cannot be Hubbard trees in any meaningful context. Later, we turn our attention to the structure of inverse limits of Hubbard trees, making use of the definition of branch point and endpoint tenured earlier in the work and demonstrate that one Hubbard tree, with minor alterations, can generate infinitely many mutually non-homeomorphic inverse limits.