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The Hausdorff Dimension of an Ergodic Invariant Measure for a Piecewise Monotonic Map of the Interval

Published online by Cambridge University Press:  20 November 2018

Franz Hofbauer  and
Peter Raith
Franz Hofbauer
Affiliation:
Institut für Mathematik Universitàt Wien Strudlhofgasse 4 A-1090 Wien, Austria
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Abstract

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We consider a piecewise monotonie and piecewise continuous map T on the interval. If T has a derivative of bounded variation, we show for an ergodic invariant measure μ with positive Ljapunov exponent λμ that the Hausdorff dimension of μ equals hμ / λμ.

Keywords

28D05.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 1 , 01 March 1992 , pp. 84 - 98
Copyright
Copyright © Canadian Mathematical Society 1992

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