Deterministic Chaos

Mathematical Definition of Chaos

For special classes of functions, Devaney's three attributes of chaos are not independent. For example,
Banks, showed that
*   if f:X → X is continuous and distances can be measured on X,
*   then sensitivity to initial conditions is a consequence of Devaney's other two conditions.
Vellekoop and Berglund showed that
*   for continuous functions taking an interval to itself,
*   the mixing condition (also called transitivity) implies the other two of Devaney's requirements.

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