Special 𝛼-limit points for maps of the interval

Hero, Michael W.

doi:10.1090/S0002-9939-1992-1100653-4

Special $\alpha$-limit points for maps of the interval
HTML articles powered by AMS MathViewer

by Michael W. Hero PDF

Proc. Amer. Math. Soc. 116 (1992), 1015-1022 Request permission

Abstract:

The notion of a special $\alpha$-limit point is defined. For maps of the interval, it is shown that a point is a special $\alpha$-limit point if and only if it is an element of the attracting center.

References

Joseph Auslander and James A. Yorke, Interval maps, factors of maps, and chaos, Tohoku Math. J. (2) 32 (1980), no. 2, 177–188. MR 580273, DOI 10.2748/tmj/1178229634
Louis Block and Ethan M. Coven, $\omega$-limit sets for maps of the interval, Ergodic Theory Dynam. Systems 6 (1986), no. 3, 335–344. MR 863198, DOI 10.1017/S0143385700003539
Hsin Chu and Jin Cheng Xiong, A counterexample in dynamical systems of the interval, Proc. Amer. Math. Soc. 97 (1986), no. 2, 361–366. MR 835899, DOI 10.1090/S0002-9939-1986-0835899-0

Continuous maps of the interval

Ethan M. Coven and G. A. Hedlund, Continuous maps of the interval whose periodic points form a closed set, Proc. Amer. Math. Soc. 79 (1980), no. 1, 127–133. MR 560598, DOI 10.1090/S0002-9939-1980-0560598-7
Ethan M. Coven and Zbigniew Nitecki, Nonwandering sets of the powers of maps of the interval, Ergodic Theory Dynam. Systems 1 (1981), no. 1, 9–31. MR 627784, DOI 10.1017/s0143385700001139
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, On a theorem of G. D. Birkhoff, Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A 1967 (1967), 429–432 (Ukrainian, with Russian and English summaries). MR 0212781
Jin Cheng Xiong, The attracting centre of a continuous self-map of the interval, Ergodic Theory Dynam. Systems 8 (1988), no. 2, 205–213. MR 951269, DOI 10.1017/S0143385700004429