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Sharkovskii's theorem - the assertion given in 1964 by the Ukrainian mathematician Alexander Nikolayevich Szarkowskiego on the occurrence of periodic points of continuous functions of the real line. This assertion is also a generalization of the Li-Yorke theorem 'on the 1975 agenda is Szarkowskiego order in the set of natural numbers, denoted, in which the lowest number is 3 and the highest 1: Let be