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Original Articles

A Proof of Sharkovsky's Theorem

Pages 373-379 | Published online: 17 Sep 2010

  • Alseda , L. , Llibre , I. and Misiurewicz , M. 2000 . Combinatorial dynamics and entropy in dimension one , Advanced Series in Nonlinear Dynamics Vol. 5 , Singapore : World Scientific .
  • Baldwin , S. 1987 . Generalizations of a theorem of Sarkovskii on orbits of continuous real-valued functions . Discrete Math , 67 : 111 – 127 .
  • Block , L. S. and Coppel , W. A. 1992 . Dynamics in One Dimension , Lecture Notes in Math Vol. 1513 , Berlin : Springer .
  • Block , L. , Guckenheimer , J. , Misiurewicz , M. and Young , L.-S. 1980 . Periodic points and topological entropy for one dimensional maps. Global theory of dynamical systems , Lecture Notes in Math Vol. 819 , 18 – 34 . Berlin : Springer .
  • Devaney , R. 1986 . An Introduction to Chaotic Dynamical Systems , Menlo Park : Benjamin/Cummings .
  • Ho , C.-W. and Morris , C. 1981 . A graph theoretic proof of Sharkovsky's theorem on the periodic points of continuous functions . Pacific J. Math. , 96 : 361 – 370 .
  • Sharkovsky , A. N. 1964 . Co-existence of the cycles of a continuous mapping of the line onto itself . Ukrain. Math. Zh. , 16 (1) : 61 – 71 .

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