Sets of recurrent points of continuous maps of the interval
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- by Jin Cheng Xiong PDF
- Proc. Amer. Math. Soc. 95 (1985), 491-494 Request permission
Abstract:
For a continuous map of the interval the following conditions are equivalent: (1) the period of every periodic point is a power of 2, (2) ${\overline R ^{( + )}} \cap {\overline R ^{( - )}} - R = \phi$, and (3) $\overline R - R$ is countable, where $R$ denotes the set of recurrent points. $\overline R$ is the closure of $R$, and ${\overline R ^{( + )}}$ (or ${\bar R^{( - )}}$) is the right-side closure (left-side closure, respectively) of $R$.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 491-494
- MSC: Primary 58F20; Secondary 54H20
- DOI: https://doi.org/10.1090/S0002-9939-1985-0806094-5
- MathSciNet review: 806094