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Existence of periodic points for maps of S\(^1\). (English) Zbl 0272.58005

MSC:
37D99 Dynamical systems with hyperbolic behavior
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References:
[1] Block, L., Franke, J.: A classification of the structurally stable contracting endomorphisms ofS 1. Proc. Amer. Math. Soc.36, 597-602 (1972) · Zbl 0263.58010
[2] Denjoy, A.: Sur les courbes définies par les équations différentielles à la surface du tore. Journal de Math. Pure et Appliquées11, 333-375 (1932) · JFM 58.1124.04
[3] Jacobson, M.V.: On smooth mappings of the circle into itself. Math. Sb.85 (127), 163-188 (1971)= Math. USSR Sb.14, 161-185 (1971)
[4] Peixoto, M.: Structural stability on two-dimensional manifolds. Topology1, 101-120 (1962) · Zbl 0107.07103
[5] Pugh, C.C.: An improved closing lemma and a general density theorem. Amer. J. Math.89, 1010-1021 (1967) · Zbl 0167.21804
[6] Smale, S.: Differentiable dynamical systems. Bull. Amer. Math. Soc.73, 747-817 (1967) · Zbl 0202.55202
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