Ledrappier-Young formula and exact dimensionality of self-affine measures

In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumpt...

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Bibliographic Details
Published in:arXiv.org 2017-07
Main Authors: Bárány, Balázs, Käenmäki, Antti
Format: Article
Language:English
Online Access:Get full text
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Summary:In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affine and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula.
ISSN:2331-8422
DOI:10.48550/arxiv.1511.05792