sensitivity to initial conditions: |
arbitrarily close to every state S_{1} of the system, there is a state S_{2}
whose future eventually is significantly different from that of S_{1}. That is
"Even the tiniest change can alter the future in ways you can't imagine.". |

dense periodic points: |
arbitrarily close to every state S_{1} of the system, there is a state S_{2}
whose future behavior eventually returns exactly to S_{2}. |

mixing: |
given any two states S_{1} and S_{2}, the
futures of some states near S_{1} eventually become near S_{2}. |