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An exceptional set in the Ergodic theory of Markov maps of the interval

Published online by Cambridge University Press:  01 July 1997

AG Abercrombie  and
R Nair
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Abstract

It is known that a Markov map $T$ of the unit interval preserves a measure $\mu$, say, equivalent to Lebesgue measure, and that almost every point of the interval has a forward orbit under $T$ that is uniformly distributed with respect to $\mu$. In the opposite direction the main result of this paper states that there is a set of points having Hausdorff dimension $1$ whose forward orbits are in a certain sense very far from being so distributed.

1991 Mathematics Subject Classification: 58F08, 28A80.

Keywords

Markov mapsHausdorff dimension
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 75 , Issue 1 , July 1997 , pp. 221 - 240
Copyright
London Mathematical Society 1997

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