### Abstract

Let ∝ be the topological space obtained by identifying the points 1 and 2 of the segment [0, 3] to a point. Let ∞ be the topological space obtained by identifying the points 0, 1 and 2 of the segment [0, 2] to a point. An ∝ (respectively ∞) map is a continuous self-map of ∝ (respectively ∞) having the branching point fixed. Set E ∈ {∝, ∞}. Let f be an E map. We denote by Per(f) the set of periods of all periodic points of f. The set K ⊂ ℕ is the full periodicity kernel of E if it satisfies the following two conditions: (1) if f is an E map and K ⊂ Per(f), then Per(f) = ℕ; (2) for each k ∈ K there exists an E map f such that Per(f) = ℕ \ {k}. In this paper we compute the full periodicity kernel of ∝ and ∞.

Original language | English |
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Pages (from-to) | 101-126 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 19 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 1999 |

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## Cite this

Leseduarte, M. C., & Llibre, J. (1999). On the full periodicity kernel for one-dimensional maps.

*Ergodic Theory and Dynamical Systems*,*19*(1), 101-126. https://doi.org/10.1017/S0143385799120984