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What is chaos theory?

What is chaos theory? Here are some definitions.

Noun
  1. (mathematics) The study of iterative non-linear systems in which arbitrarily small variations in initial conditions become magnified over time.
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It is a straightforward popular science treatment of the mathematics and science behind chaos theory.
That the tiniest thing can sometimes decide the future course of events is not a discovery exclusive to chaos theory.
Mathematician benoit Mandelbrot is namedropped on page 49 in a hiccupped discussion of chaos theory.
We'll have to forgive him for forgetting that it's chaos theory, not catastrophe theory.
One criticism often laid at the door of chaos theory is that little progress has been made in this discipline after its stunning start.
Yet true to chaos theory, the appearance of non-linearity does not necessarily imply a lack of coherent structures.

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