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Local dimension for piecewise monotonic maps on the interval

Published online by Cambridge University Press:  14 October 2010

Franz Hofbauer
Franz Hofbauer
Affiliation:
Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
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Abstract

The local dimension of invariant and conformal measures for piecewise monotonic transformations on the interval is considered. For ergodic invariant measures m with positive characteristic exponent χm we show that the local dimension exists almost everywhere and equals hm/χm For certain conformal measures we show a relation between a pressure function and the Hausdorff dimension of sets, on which the local dimension is constant.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 6 , December 1995 , pp. 1119 - 1142
Copyright
Copyright © Cambridge University Press 1995

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