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For a map , a point is periodic with period if and for all . When is continuous and is an interval, a theorem due to Sharkovskii () states that there is an order in , say , such that if has a periodic point of period and , then also has a periodic point of period . In this work, we will see how an extension of the order to sequences of positive integers yields a Sharkovskii-type result for non-wandering points of .
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Maria Pires de Carvalho, Fernando Jorge Moreira, Sharkovskii order for non-wandering points. Port. Math. 69 (2012), no. 2, pp. 159–165DOI 10.4171/PM/1911