Discrete Dynamical Systems

This book provides an introduction to the analysis of discrete dynamical systems. It analyzes the fundamental factors that govern the quantitative and qualitative behavior of 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 explicit solutions. The analysis focuses initially on the derivation of basic propositions about the factors that governs the evolution of a state variable in the elementary context of a one-dimensional, first-order, linear autonomous system. These basic propositions are subsequently generalized to account for the analysis of multi-dimensional, non-linear, higher-order, non-autonomous dynamical systems.