Deterministic Chaos

Mathematical Definition of Chaos

For special classes of functions, Devaney's three attributes of chaos are not independent. For example,

Banks, et.al. 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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