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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the existence of conformal measures


Authors: Manfred Denker and Mariusz Urbański
Journal: Trans. Amer. Math. Soc. 328 (1991), 563-587
MSC: Primary 58F11; Secondary 28A12, 28A78, 28D05
DOI: https://doi.org/10.1090/S0002-9947-1991-1014246-4
MathSciNet review: 1014246
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Abstract: A general notion of conformal measure is introduced and some basic properties are studied. Sufficient conditions for the existence of these measures are obtained, using a general construction principle. The geometric properties of conformal measures relate equilibrium states and Hausdorff measures. This is shown for invariant subsets of $ {S^1}$ under expanding maps.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1014246-4
Article copyright: © Copyright 1991 American Mathematical Society