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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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


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
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 308 (1988), 227-241
  • MSC: Primary 58F30; Secondary 34C35
  • DOI:
  • MathSciNet review: 946440