# Dynamics in one real variable

# Dynamics in one real variable

Discrete time dynamics is simply the repeated action of the same function. Surprisingly, even the simplest case of the iteration of a function of one real variable can lead to chaos. This chapter introduces the idea of a fixed point, and its stability. Cobweb diagrams are used to visualize orbits. The doubling map is an example of chaos. Feigenbaum's period doubling approach to chaos is explained at an elementary level. Examples of invariance measures are given.

*Keywords:*
iteration, fixed point, stability, cobweb diagram, chaos, period doubling, invariance measures

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