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Simple mathematical models with very complicated dynamics. (English) Zbl 1369.37088
Summary: First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.

MSC:
37N25 Dynamical systems in biology
37N40 Dynamical systems in optimization and economics
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