Sharkovskii's theorem

In mathematics, Sharkovskii's theorem (also spelled Sharkovsky, Sharkovskiy, Šarkovskii or Sarkovskii), named after Oleksandr Mykolayovych Sharkovsky, who published it in 1964, is a result about discrete dynamical systems.^[1] One of the implications of the theorem is that if a discrete dynamical system on the real line has a periodic point of period 3, then it must have periodic points of every other period.

^ Sharkovskii, A. N. (1964). "Co-existence of cycles of a continuous mapping of the line into itself". Ukrainian Math. J. 16: 61–71.

[1] Sharkovskii, A. N. (1964). "Co-existence of cycles of a continuous mapping of the line into itself". Ukrainian Math. J. 16: 61–71.

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