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A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamics
Contains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations
Has an extensive number of applications in a variety of fields from neural network to host-parasitoid systems
Includes chapters on continued fractions, orthogonal polynomials and asymptotics
Lucid and transparent writing style
The second edition has greatly benefited from a sizable number of comments and suggestions I received from users of the book. I hope that I have corrected all the er rors and misprints in the book. Important revisions were made in Chapters I and 4. In Chapter I, we added two appendices (global stability and periodic solutions). In Chapter 4, we added a section on applications to mathematical biology. Influenced by a friendly and some not so friendly comments about Chapter 8 (previously Chapter 7: Asymptotic Behavior of Difference Equations), I rewrote the chapter with additional material on Birkhoff's theory. Also, due to popular demand, a new chapter (Chapter 9) under the title "Applications to Continued Fractions and Orthogonal Polynomials" has been added. This chapter gives a rather thorough presentation of continued fractions and orthogonal polynomials and their intimate connection to second-order difference equations. Chapter 8 (Oscillation Theory) has now become Chapter 7. Accordingly, the new revised suggestions for using the text are as follows. The diagram on p. viii shows the interdependence of the chapters The book may be used with considerable flexibility. For a one-semester course, one may choose one of the following options: (i) If you want a course that emphasizes stability and control, then you may select Chapters I, 2, 3, and parts of 4, 5, and 6. This is perhaps appropriate for a class populated by mathematics, physics, and engineering majors.
1 Dynamics of First-Order Difference Equations.- 2 Linear Difference Equations of Higher Order.- 6 Control Theory.- 8 Asymptotic Behavior of Difference Equations.- 9 Applications to Continued Fractions and Orthogonal Polynomials.- Answers to Selected Problems.- Maple Programs.- Appendix C Classical Orthogonal Polynomials.- Appendix D Identities and Formulas.