Local dimension for piecewise monotonic maps on the interval

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 me...

Full description

Saved in:
Bibliographic Details
Published in:Ergodic theory and dynamical systems 1995-12, Vol.15 (6), p.1119-1142
Main Author: Hofbauer, Franz
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0143-3857
1469-4417
DOI:10.1017/S0143385700009822