Remarks on Sharkovsky's Theorem

American Mathematical Monthly

Volumn 104, Issue 9, 1997, Pages 846-847

  Misiurewicz, Michał ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031484982     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.2307/2975290     Document Type: Article

References (16)

1. L. Alsedà, J. Llibre, and M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One, Adv. Ser. in Nonlinear Dynamics 5, World Scientific, Singapore, 1993.
2. L. Alsedà, J. Llibre, and R. Serra, Minimal periodic orbits for continuous maps of the interval, Trans. Amer. Math. Soc., 286 (1984), 595-627.
3. L. Block, J. Guckenheimer, M. Misiurewicz, and L.-S. Young, Periodic points and topological entropy of one dimensional maps, Global Theory of Dynamical Systems, Lecture Notes in Math., 819, Springer, Berlin, 1980, pp. 18-34.
4. U. Burkart, Interval mapping graphs and periodic points of continuous functions, J. Combin. Theory Ser. B, 32 (1982), 57-68.
5. P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Progr. in Phys. 1, Birkhäuser, Boston, 1980.
6. W. A. Coppel, Šarkovskii-minimal orbits, Math. Proc. Cambr. Phil. Soc. 93 (1983), 397-408.
7. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Second Edition, Addison-Wesley, Redwood City, California, 1989.
8. S. Elaydi, On a converse of Sharkovsky's Theorem, Amer. Math. Monthly 103 (1996), 386-392.
9. C.-W. Ho, On the structure of the minimum orbits of periodic points for maps of the real line, preprint, Southern Illinois Univ., Edwardsville, IL (1984).
10. C.-W. Ho and C. Morris, A graph theoretic proof of Sharkovsky's theorem on the periodic points of continuous functions, Pacific J. Math. 96 (1981), 361-370.
11. T.-Y. Li and J. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), 985-992.
12. A. N. Sharkovsky, Co-existence of the cycles of a continuous mapping of the line into itself, Ukrain. Math. Zh. 16 (1) (1964), 61-71 (Russian).
13. A. N. Sharkovsky, Coexistence of the cycles of a continuous mapping of the line into itself, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 5 (1995), 1263-1273.
14. A. N. Sharkovsky, On cycles and structure of a continuous map, Ukrain. Math. Zh. 17 (3) (1965), 104-111 (Russian).
15. P. Stefan, A theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line, Comm. Math. Phys. 54 (1977), 237-248.
16. P. D. Straffin Jr., Periodic points of continuous functions, Math. Mag. 51 (1978), 99-105.