Geodesic
Periodic Points and Contractive Mappings
Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 209-211

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Let X be a non-empty set and f:X→X. A point x ∈ X is (i) a fixed point off f(x)=x, and (ii) a periodic point of f iff there is a positive integer N such that fN(x)=x. Also a periodic orbit of f is the (finite) set {x, f(x), f2(x),...} where x is a periodic point of f. 
Hsieh, Tsu-Teh; Tan, Kok-Keong. Periodic Points and Contractive Mappings. Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 209-211. doi: 10.4153/CMB-1974-042-3
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     title = {Periodic {Points} and {Contractive} {Mappings}},
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     doi = {10.4153/CMB-1974-042-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-042-3/}
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