In recent years there has been unprecedented popular interest in the chaotic behaviour of discrete dynamical systems. The ease with which a modest microcomputer can produce graphics of extraordinary complexity has fired the interest of mathemaiiealh-minded people from pupils in schools to postgraduate students. At undergraduate level, there is a need to give a basic account of the computed complexity within a recognized framework of mathematu .;! theory. In producing this replacement for Ordinary Differential Equations \ODK) we have responded to this need by extending our treatment of the qualitative behaviour of differential equations.
This Ь.чк is aimed at second and third year undergraduate students who have completed first courses in Calculus of Several Variables and Linear Algebra. Our approach is to use examples to illustrate the significance of the results piesenled. 'I he text is supported by a mix of manageable and challenging exercises that give readers the opportunity to both consolidate and develop the ideas they encounter. As in ODE, we wish to highlight the significance of important theorems, to show how they are used and to stimulate interest sn a deeper understanding of them.
We have retained our earlier introduction and discussion of linear systems (Chapters 1 and 2). Our treatment of non-linear differential equations has been extended to include Poincarc maps and phase spaces of dimension greater than two (Chapters 3 and 4). Applications involving planar phase spaces leo\ered in Chapter 4 of ODE) appear in Chapter 5. Problems involving non-planar phase spaces and families of systems are considered in Chapter ft. where elementary bifurcation theory is introduced and its application to chaotic behaviour is examined. Although ordinary differential equations icmain the dnuug fmcc behind the book, a substantial part of the new material concerns discrete dynamical systems and the title Ordinary Dillt-i-fniutl l.tfiiimtHr. r iio ioni'ci appropriate. We have therefore chosen a new title lor the extended text that clarifies its connection with the broader field of dynamical systems,
