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.