A point is called Cʳ preperiodic if it can be made periodic via arbitrarilysmall Cʳ perturbation. We discuss some general properties of the Cʳ preperiodic set,and prove that the C¹ preperiodic set contains noobstruction points if and onlyif the system is Axiom A plus no-cycle.
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Lan Wen (2000) studied this question.
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