Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T03:37:41.559Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)