Pseudo-orbit shadowing in the family of tent maps
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- by Ethan M. Coven, Ittai Kan and James A. Yorke PDF
- Trans. Amer. Math. Soc. 308 (1988), 227-241 Request permission
Abstract:We study the family of tent maps—continuous, unimodal, piecewise linear maps of the interval with slopes $\pm s$, $\sqrt 2 \leqslant s \leqslant 2$. We show that tent maps have the shadowing property (every pseudo-orbit can be approximated by an actual orbit) for almost all parameters $s$, although they fail to have the shadowing property for an uncountable, dense set of parameters. We also show that for any tent map, every pseudo-orbit can be approximated by an actual orbit of a tent map with a perhaps slightly larger slope.
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- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 308 (1988), 227-241
- MSC: Primary 58F30; Secondary 34C35
- DOI: https://doi.org/10.1090/S0002-9947-1988-0946440-2
- MathSciNet review: 946440