An Introduction to Difference Equations von Saber Elaydi

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

* Preface * List of Symbols * Dynamics of First-Order Difference Equations * Linear Difference Equations of Higher Order * Systems of Linear Difference Equations * Stability Theory * Higher Order Scalar Difference Equations * The Z-Transform Method and Volterra Difference Equations *Oscillation Theory * Asymptotic Behavior of Difference Equations * Applications to Continued Fractions and Orthogonal Polynomials * Control Theory * Answers and Hints to Selected Problems * Appendix A: Stability of Nonhyperbolic Fixed Points of Maps on the Real Line * Vandermonde Matrix * Stability of Nondifferentiable Maps * Stable Manifold and Hartman-Grobman-Cushing Theorems * Levin-May Theorem * Classical Orthogonal Polynomials * Identities and Formulas * References * Index