Introduction to the 2008 Re - Publication of the “ Neimark - Sacker Bifurcation Theorem ”

We give a brief introduction to re-publication of Chapter 2 of the author’s 1964 Dissertation. The result has come to be known as the Neimark-Sacker bifurcation theorem. Some of the applications of the theorem are cited and a brief overview of the reduction of the mapping to normal form is given in 3-dimensions. By introducing weighted monomials the reduction method is carried out without the use of the Center Manifold theorem which was not known to the author and was published the same year as the dissertation. The first detailed proof of the theorem is carried out in the above cited Chapter 2 and is contained in the companion article to follow this one.