Exploring the Theory of Geometric Bifurcation

This paper will deal with the Theory of Geometric Bifurcation, which the author developed in 1986. The theory developed in those papers is very general and abstract. So, until a symbolic software program such as Mathematica came along, it was very difficult to examine concrete examples that would illustrate and explain the theory. In this paper we will look at examples of bifurcating branches of solutions of the nonlinear: algebraic equations, ordinary differential equations, and partial differential equations.