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Equilibrium States and Hausdorff Measures for Interval Maps

✍ Scribed by Franz Hofbauer; Gerhard Keller

Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 936 KB
Volume: 164
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19931640117

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✦ Synopsis

Abstract

For a class of piecewise monotone interval maps T (including unimodal maps with negative Schwarzian derivative) and real valued functions f of bounded variation we compare equilibrium states μ of f with Hausdorff measures v and give an integral test for the dichotomy μ ≪ v or μ ⊥ v. For certain classes of rational maps such a result was proved in [15] and [3].

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