# American Institute of Mathematical Sciences

January  2000, 6(1): 237-241. doi: 10.3934/dcds.2000.6.237

## On the preperiodic set

 1 School of Mathematic Sciences, Peking University, Beijing, 100871

Received  November 1999 Published  December 1999

A point is called $C^r$ preperiodic if it can be made periodic via arbitrarily small $C^r$ perturbation. We discuss some general properties of the $C^r$ preperiodic set, and prove that the $C^1$ preperiodic set contains no obstruction points if and only if the system is Axiom A plus no-cycle.
Citation: Lan Wen. On the preperiodic set. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 237-241. doi: 10.3934/dcds.2000.6.237
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