The full periodicity kernel of the trefoil
Annales de l'Institut Fourier, Tome 46 (1996) no. 1, p. 219-262
We consider the following topological spaces: O={z:|z+i|=1}, O 3 =O{z:z 4 [0,1],Imz0}, O 4 =O{z:z 4 [0,1]}, 1 =O:|z-i|=1}{z:z[0,1]}, 2 = 1 {z:z 2 [0,1]}, et T={z:z= cos (3θ)e iθ ,0θ2π}. 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 is the full periodicity kernel of E if it satisfies the following two conditions: (1) If f is an E map and KPer(f), then Per(f)=. (2) If S is a set such that for every E map f, SPer(f) implies Per(f)=, then KS. In this paper we compute the full periodicity kernel of O 3 ,O 4 , 1 , 2 and T.
@article{AIF_1996__46_1_219_0,
     author = {Leseduarte, Carme and Llibre, Jaume},
     title = {The full periodicity kernel of the trefoil},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {46},
     number = {1},
     year = {1996},
     pages = {219-262},
     doi = {10.5802/aif.1512},
     zbl = {0834.54024},
     mrnumber = {1385516},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1996__46_1_219_0}
}
Leseduarte, Carme; Llibre, Jaume. The full periodicity kernel of the trefoil. Annales de l'Institut Fourier, Tome 46 (1996) no. 1, pp. 219-262. doi : 10.5802/aif.1512. http://www.numdam.org/item/AIF_1996__46_1_219_0/

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