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Some results on the Šarkovskiĭ\ partial ordering of permutations

1991
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Transactions of the American Mathematical Society
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If n is a cyclic permutation and x is a periodic point of a continuous function /:R •-► R with period(x) = order(Tt) = n , then we say that x has type n if the orbit of x consists of points xx < x2 < •■■ < xn with f(x¡) = x"/« . In analogy with Sarkovskii's Theorem, we define a partial ordering on cyclic permutations by 8 -» n if every continuous function with a periodic point of type 0 also has a point of type n . In this paper we examine this partial order form the point of view of critical

doi:10.1090/s0002-9947-1991-0998354-x
fatcat:lnlaz6hjkvbsjlm53l3avgoec4