As we all know, Devaney for Chaos is defined as:
For mapping F, satisfied if: 1) First worth of sensitive dependence; 2) transmission of topology; 3) dense periodic points.
We can say that the mapping F is chaotic.
So these three conditions how should we understand it?
1) From the viewpoint of stability, chaotic orbit is a partially unstable, "sensitive First condition" is the description of such chaotic orbit instability. For sensitivity to initial conditions, means that no matter X, Y just how close, in the role of F, the two tracks are likely to separate from a greater distance, and in the vicinity of each point X can be found near him Also under the effect of the final split point F Y. For such F., If its orbit calculated by the computer, any small initial error, after a few iterations will result in the failure of the calculation result.
2) transitivity means that at any point in the field under the effect of F will "walk" across metric space V, it can not be described or segment F can not be decomposed into two subsystems do not affect each other at F.
3) General features of the above two random system, but the third - dense set of periodic points, but that the system has a strong and regularity certainty, not a disorder, but the shape of disorders actually ordered, which is capable of chaos and other applied disciplines to combine premise applications.