On the existence of conformal measures

Denker, Manfred; Urbański, Mariusz

doi:10.1090/S0002-9947-1991-1014246-4

On the existence of conformal measures
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by Manfred Denker and Mariusz Urbański

Trans. Amer. Math. Soc. 328 (1991), 563-587

DOI: https://doi.org/10.1090/S0002-9947-1991-1014246-4

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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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