On a Change of Variables which Varies Continuously in the Perturbation Parameter

摘要

During the summer of 1963 at the University of Colorado in Boulder, Professor S. P. Diliberto [1] gave lectures on perturbation theory of ordinary differential equations. Included in his lectures was the reduction of two dimensional systems of ordinary differential equa¬tions in a neighborhood of a periodic solution to certain normal forms. The theorem presented below is the end process in a certain reduction.