On the existence of conformal measures

Manfred Denker; Mariusz Urbański

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

On the existence of conformal measures

Manfred Denker, Mariusz Urbański

Mathematics

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109 Scopus citations

Abstract

A general notion of conformai 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 conformai measures relate equilibrium states and HausdorfF measures. This is shown for invariant subsets of S¹ under expanding maps.

Original language	English (US)
Pages (from-to)	563-587
Number of pages	25
Journal	Transactions of the American Mathematical Society
Volume	328
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1991-1014246-4
State	Published - Dec 1991

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-1991-1014246-4

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abstract = "A general notion of conformai 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 conformai measures relate equilibrium states and HausdorfF measures. This is shown for invariant subsets of S1 under expanding maps.",

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AB - A general notion of conformai 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 conformai measures relate equilibrium states and HausdorfF measures. This is shown for invariant subsets of S1 under expanding maps.

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On the existence of conformal measures

Abstract

All Science Journal Classification (ASJC) codes

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