Discrete Dynamical Systems

✍ Scribed by Prof. Oded Galor (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2007
• Tongue: English
• Leaves: 163
• Edition: 1
• Category: Library

✦ Synopsis

This book provides an introduction to discrete dynamical systems -- a framework of analysis commonly used in the fields of biology, demography, ecology, economics, engineering, finance, and physics. The book characterizes the fundamental factors that govern the qualitative and quantitative trajectories of a variety of deterministic, discrete dynamical systems, providing solution methods for systems that can be solved analytically and methods of qualitative analysis for systems that do not permit or necessitate an explicit solution. The analysis focuses initially on the characterization of the factors the govern the evolution of state variables in the elementary context of one-dimensional, first-order, linear, autonomous systems. The fundamental insights about the forces that affect the evolution of these elementary systems are subsequently generalized, and the determinants of the trajectory of multi-dimensional, nonlinear, higher-order, non-autonomous dynamical systems are established.

✦ Table of Contents

One-Dimensional, First-Order Systems....Pages 1-26
Multi-Dimensional, First-Order, Linear Systems: Solution....Pages 27-58
Multi-Dimensional, First-Order, Linear Systems: Characterization....Pages 59-91
Multi-Dimensional, First-Order, Nonlinear Systems....Pages 93-105
Higher-Order and Non-Autonomous Systems....Pages 107-113
Examples of Two-Dimensional Systems....Pages 115-145

✦ Subjects

Game Theory/Mathematical Methods;Dynamical Systems and Ergodic Theory;Complexity