- 3 <= 5 <= 7 <= 9 <= ... <= 2·3 <= 2·5 <= 2·7 <= ... <= 2
^{2}·3 <= 2^{2}·5 <= ..... <= 2^{4}<= 2^{3}<= 2^{2}<= 2 <= 1.

- If
*f*has a periodic point of period*m*and*m*<=*n*in the above ordering, then*f*has also a periodic point of period*n*.

Sarkovskii's theorem does not state that there are *stable* cycles of those periods, just that there are cycles of those periods. For systems such as the logistic map, the bifurcation diagram shows a range of parameter values for which apparently the only cycle has period 3. In fact, there must be cycles of all periods there, but they are not stable and therefore not visible on the computer generated picture.

Interestingly, the above "Sarkovskii ordering" of the positive integers also occurs in a slightly different context in connection with the logistic map: the *stable* cycles appear in this order in the bifurcation diagram, starting with 1 and ending with 3, as the parameter is increased. (Here we ignore a stable cycle if a stable cycle of the same order has occurred earlier.)