ABSTRACT
Chaos, in the mathematical sense, was first encountered in the 1960s independently by a variety mathematicians and the mathematically inclined scientists. One common nomenclature is to use the suffix “morphism” when describing a function. A one-to-one function is called a monomorphism. A function that is both one-to-one and onto is called a homeomorphism.Using the homeomorphism to establish the topological equivalence of the spaces is only half of the problem. The mathematicians also need to establish dynamical equivalence of the functions being iterated. This is done by looking at the interaction between the dynamical functions and the homeomorphism as represented in the commutative diagram.
