Deterministic Chaos

Mathematical Definition of Chaos

The term "chaos" seems first to have been used by Li and Yorke.

They prove that if a function f:[0,1] -> [0,1] has a 3-cycle, then f is chaotic in this sense:

it has periodic points of all periods,

and there is an infinite collection of non-periodic points with iterates that approach one another arbitrarily closely, only to move far away again, and that never approach and remain near any periodic point.

Return to Mathematical Definition of Chaos.