Deterministic Chaos

6.B. Introduction to Chaos

Devaney characterizes deterministic chaos by three properties
sensitivity to initial conditions: arbitrarily close to every state S1 of the system, there is a state S2 whose future eventually is significantly different from that of S1. That is "Even the tiniest change can alter the future in ways you can't imagine.".
dense periodic points: arbitrarily close to every state S1 of the system, there is a state S2 whose future behavior eventually returns exactly to S2.
mixing: given any two states S1 and S2, the futures of some states near S1 eventually become near S2.
The mathematical formulation of these properties will be illustrated using simple functions.

Return to Introduction to Chaos.