Abstract:We introduce a continuous function from [0, 1] onto itself whose nonwandering set is the Cantor ternary set $C$. This function is also chaotic in the sense of Li and Yorke, but with the property that almost all points of [0, 1] are eventually fixed. Those points of $C$ which are periodic, eventually periodic, asymptotically periodic or recurrent are also explicitly identified.
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- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 277-278
- MSC: Primary 58F13; Secondary 26A30, 54H20
- DOI: https://doi.org/10.1090/S0002-9939-1984-0754720-0
- MathSciNet review: 754720