Chaos and the Dynamics of Quadratic Mappings

Abstract

The immediate aim of this paper is to systematically investigate dynamical systems governed by a certain class of difference equations. The results obtained do not, however, constitute an isolated piece in a sprawling typology of dynamical systems. Instead, the phenomena encountered in our setting are often, with appropriate modifications, characteristic of all dynamical systems. Exploring these analogies is a secondary aim of this paper. The type of dynamical system that forms the basis of our inquiry is without question the best "window" upon dynamical phenomena in general. The study of dynamical systems involving, say, differential equations requires a higher degree of mathematical sophistication, and is at the same time more cluttered. Certain phenomena present in the simplest (onedimensional) systems involving difference equations have no parallels in continuous dynamical systems involving less than three coupled differential equations. [From Preface]