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

DOI:
https://doi.org/10.1090/S0002-9947-1988-0946440-2

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 , . We show that tent maps have the shadowing property (every pseudo-orbit can be approximated by an actual orbit) for almost all parameters , 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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DOI:
https://doi.org/10.1090/S0002-9947-1988-0946440-2

Article copyright:
© Copyright 1988
American Mathematical Society