## Abstract

We look at density of periodic points and Devaney Chaos. We prove that if f is

Devaney Chaotic on a compact metric space with no isolated points, then the set of points with prime period at least n is dense for each n. Conversely, we show that if f is a continuous function from a closed interval to itself, for which the set of points with prime period at least n is dense for each n, then there is a decomposition of the interval into closed subintervals on which either f or f 2 is Devaney Chaotic. (In fact, this result holds if the set of points with prime period at least 3 is dense.)

Devaney Chaotic on a compact metric space with no isolated points, then the set of points with prime period at least n is dense for each n. Conversely, we show that if f is a continuous function from a closed interval to itself, for which the set of points with prime period at least n is dense for each n, then there is a decomposition of the interval into closed subintervals on which either f or f 2 is Devaney Chaotic. (In fact, this result holds if the set of points with prime period at least 3 is dense.)

Original language | English |
---|---|

Pages (from-to) | 773-780 |

Number of pages | 8 |

Journal | The American Mathematical Monthly |

Volume | 122 |

Issue number | 8 |

DOIs | |

Publication status | Published - Oct 2015 |