Sharkovsky's Theorem

Sharkovsky’s Theorem, first proved in 1964, is an incredibly powerful and beautiful strengthening of the Period-3 Theorem. In 1964, O. N. Sharkovsky published a short paper that included this theorem that now bears his name. Originally published in Russian, this paper remained unknown in the West until Li and Yorke published their result ten years later. Together, these two papers have revolutionized the field of dynamical systems.