Introduction and Simple Properties

Abstract

In 1963 E. N. Lorenz wrote a remarkable paper. In it he described a three parameter family of three-dimensional ordinary differential equations which appeared, when integrated numerically on a computer, to have extremely complicated solutions. These equations, now known as the Lorenz equations, have been studied by many authors in the years since 1963 and one of our aims, in these notes, is to contribute to this study. It is necessary, therefore, to explain some of the reasons why the equations generated so much interest initially and why they warrant further study.