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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Pseudo-orbit shadowing in the family of tent maps


Authors: Ethan M. Coven, Ittai Kan and James A. Yorke
Journal: Trans. Amer. Math. Soc. 308 (1988), 227-241
MSC: Primary 58F30; Secondary 34C35
MathSciNet review: 946440
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0946440-2
PII: S 0002-9947(1988)0946440-2
Article copyright: © Copyright 1988 American Mathematical Society