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First Course in Discrete Dynamical Systems
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This book is intended to introduce the reader both to topics in dynamical systems and mathematical thinking. In particular, the authors emphasize those portions of mathematical analysis necessary for understanding the intricacies of a discrete dynamical system. The organizing principle is the development of an understanding of the parametrized family of functions h(x) = rx(1-x). The readers should have some background in calculus though they need not have an extensive background in proof based mathematics. Students will learn to understand periodic points, stable sets, bifurcations, symbolic dynamics, chaos. This book includes rigorous proofs of important concepts in dynamics and is still accessible to the typical advanced undergraduate student.§
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