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Periodic orbits, entropy, and rotation sets of continuous mappings of the circle

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Literature cited

  1. R. Ito, “Rotation sets are closed,” Math. Proc. Camb. Phil. Soc.,89, No. 1, 107–111 (1981).

    Google Scholar 

  2. A. N. Sharkovskii, “Coexistence of cycles for a continuous transformation of the line into itself,” Ukr. Mat. Zh.,16, No. 1, 61–71 (1964).

    Google Scholar 

  3. L. S. Efremova, “Periodic orbits and degree of a continuous mapping of the circle,” Differents. Integr. Uravn.,2, 109–115 (1978).

    Google Scholar 

  4. L. Block, J. Guckenheimer, M. Misiurewicz, and L. S. Young, “Periodic points and topological entropy,” in: Lect. Notes Math.,819, 18–34 (1980).

    Google Scholar 

  5. L. Block, “Periods of periodic points of maps of the circle which have a fixed point,” Proc. Am. Math. Soc.,82, No. 3, 481–486 (1981).

    Google Scholar 

  6. J. Auslander and Y. Katznelson, “Continuous maps on the circle without periodic points,” Isr. J. Math.,32, No. 4, 375–381 (1979).

    Google Scholar 

  7. Z. Nitecki, Differentiable Dynamics. An Introduction to the Orbit Structure of Diffeomorphisms, MIT Press, Cambridge, Massachusetts (1971).

    Google Scholar 

  8. V. S. Afraimovich, “Some properties of the topological entropy,” in: Trudy V Mezhdunar. Konf. po Nelin. Kolebaniyam, Vol. 1, Naukova Dumka, Kiev (1970).

    Google Scholar 

  9. V. M. Alekseev, “Symbolic dynamics,” in: XI Mat. Shkola, Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1976).

    Google Scholar 

  10. R. L. Adler, A. G. Konheim, and M. H. McAndrew, “Topological entropy,” Trans. Am. Math. Soc.,114, No. 2, 309–319 (1965).

    Google Scholar 

  11. K. Prachar, Primzahlverteilung, Springer-Verlag, Berlin (1957).

    Google Scholar 

  12. M. Misiurewicz, “Horseshoes for mappings of the interval,” Bull. Acad. Pol. Sci.,27, No. 2, 167–169 (1979).

    Google Scholar 

  13. L. S. Efremova and R. G. Rachmankulov, “Coexistence theorems for periodic points of endomorphisms of the circle,” Differents. Integr. Uravn.,4, 116–118 (1980).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 35, No. 3, pp. 327–332, May–June, 1983.

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Malkin, M.I. Periodic orbits, entropy, and rotation sets of continuous mappings of the circle. Ukr Math J 35, 280–285 (1983). https://doi.org/10.1007/BF01092176

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  • DOI: https://doi.org/10.1007/BF01092176

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