### Abstract

Let σ be the topological space formed by the points (x, y) of R2 such that either x2 + y2 = 1, or 0 ≤ x ≤ 2 and y = 1. A σ map f(hook) is a continuous self-map of σ having the branching point (0, 1) as a fixed point. We denote by Per(f(hook)) the set of periods of all periodic points of f(hook), and by N the set of positive integers. We prove that if f(hook) is a σ map and (2, 3, 4, 5, 7) ⊆ Per(f(hook)), then Per(f(hook)) = N. Conversely, if S ⊆ N is a set such that for every σ map f(hook) S ⊆ Per(f(hook)) implies Per(f(hook)) = N, then (2, 3, 4, 5, 7) ⊆ S. © 1994 Academic Press, Inc.

Original language | English |
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Pages (from-to) | 639-651 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 183 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 1994 |

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## Cite this

Llibre, J., Paraños, J., & Rodriguez, J. A. (1994). The Full Periodicity Kernel for σ Maps.

*Journal of Mathematical Analysis and Applications*,*183*(3), 639-651. https://doi.org/10.1006/jmaa.1994.1171