On Block’s condition for simple periodic orbits of functions on an interval

Ho, Chung-Wu

doi:10.1090/S0002-9947-1984-0722777-3

On Block’s condition for simple periodic orbits of functions on an interval
HTML articles powered by AMS MathViewer

by Chung-Wu Ho PDF

Trans. Amer. Math. Soc. 281 (1984), 827-832 Request permission

Abstract:

Recently, L. Block has shown that for any mapping $f$ of an interval, whether $f$ has a periodic point whose period contains an odd factor greater than $1$ depends entirely on the periodic orbits of $f$ whose periods are powers of $2$. In this paper the author shows that Block’s result is a special case of a more general phenomenon.

References

Louis Block, Simple periodic orbits of mappings of the interval, Trans. Amer. Math. Soc. 254 (1979), 391–398. MR 539925, DOI 10.1090/S0002-9947-1979-0539925-9
Louis Block, John Guckenheimer, MichałMisiurewicz, and Lai Sang Young, Periodic points and topological entropy of one-dimensional maps, Global theory of dynamical systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979) Lecture Notes in Math., vol. 819, Springer, Berlin, 1980, pp. 18–34. MR 591173

On the structure of the minimum orbits of periodic points for maps of the real line

Chung Wu Ho and Charles Morris, A graph-theoretic proof of Sharkovsky’s theorem on the periodic points of continuous functions, Pacific J. Math. 96 (1981), no. 2, 361–370. MR 637977, DOI 10.2140/pjm.1981.96.361
Zbigniew Nitecki, Topological dynamics on the interval, Ergodic theory and dynamical systems, II (College Park, Md., 1979/1980), Progr. Math., vol. 21, Birkhäuser, Boston, Mass., 1982, pp. 1–73. MR 670074
O. M. Šarkovs′kiĭ, Co-existence of cycles of a continuous mapping of the line into itself, Ukrain. Mat. . 16 (1964), 61–71 (Russian, with English summary). MR 0159905
P. Štefan, A theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line, Comm. Math. Phys. 54 (1977), no. 3, 237–248. MR 445556, DOI 10.1007/BF01614086
Philip D. Straffin Jr., Periodic points of continuous functions, Math. Mag. 51 (1978), no. 2, 99–105. MR 498731, DOI 10.2307/2690145