no. 1
The full periodicity kernel of the trefoil
Annales de l'Institut Fourier, Volume 46 (1996) no. 1, pp. 219-262.

We consider the following topological spaces: O={z∈ℂ:|z+i|=1}, O 3 =O∪{z∈ℂ:z 4 ∈[0,1],Imz≥0}, O 4 =O∪{z∈ℂ:z 4 ∈[0,1]}, ∞ 1 =O:|z-i|=1}∪{z∈ℂ:z∈[0,1]}, ∞ 2 =∞ 1 ∪{z∈ℂ:z 2 ∈[0,1]}, et T={z∈ℂ:z= cos (3θ)e iθ ,0≤θ≤2π}. Set E∈{O 3 ,O 4 ,∞ 1 ,∞ 2 ,T}. An E map f is a continuous self-map of E having the branching point fixed. 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) If S⊂ℕ is a set such that for every E map f, S⊂Per(f) implies Per(f)=ℕ, then K⊂S. In this paper we compute the full periodicity kernel of O 3 ,O 4 ,∞ 1 ,∞ 2 and T.

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Leseduarte, Carme; Llibre, Jaume. The full periodicity kernel of the trefoil. Annales de l'Institut Fourier, Volume 46 (1996) no. 1, pp. 219-262. doi : 10.5802/aif.1512. https://aif.centre-mersenne.org/articles/10.5802/aif.1512/

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