An introduction to both topics in dynamical systems and mathematical thinking. In particular, the authors emphasize those parts of mathematical analysis necessary for understanding the intricacies of a discrete dynamical system. The organizing principle is the understanding of the parametrized family of functions h(x) = rx(1-x). Readers should have some background in calculus although extensive knowledge of proof-based mathematics is not necessary. Students will learn to understand periodic points, stable sets, bifurcations ...
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An introduction to both topics in dynamical systems and mathematical thinking. In particular, the authors emphasize those parts of mathematical analysis necessary for understanding the intricacies of a discrete dynamical system. The organizing principle is the understanding of the parametrized family of functions h(x) = rx(1-x). Readers should have some background in calculus although extensive knowledge of proof-based mathematics is not necessary. Students will learn to understand periodic points, stable sets, bifurcations, symbolic dynamics, and chaos. The book includes rigorous proofs of important concepts in dynamics while remaining accessible to the typical advanced undergraduate.
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