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ON THE EVENTUAL PERIODICITY OF PIECEWISE LINEAR CHAOTIC MAPS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 95 / Issue 3 / June 2017
- Published online by Cambridge University Press:
- 16 February 2017, pp. 467-475
- Print publication:
- June 2017
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- Article
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We present a family of continuous piecewise linear maps of the unit interval into itself that are all chaotic in the sense of Li and Yorke [‘Period three implies chaos’, Amer. Math. Monthly82 (1975), 985–992] and for which almost every point (in the sense of Lebesgue) in the unit interval is an eventually periodic point of period
$p,p\geq 3$, for a member of the family.
