Ledrappier-Young formula and exact dimensionality of self-affine measures
Bárány, B., & Käenmäki, A. (2017). Ledrappier-Young formula and exact dimensionality of self-affine measures. Advances in Mathematics, 318(1), 88-129. https://doi.org/10.1016/j.aim.2017.07.015
Published inAdvances in Mathematics
© 2017 Elsevier Inc. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.
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.
Publication in research information system
MetadataShow full item record
Showing items with similar title or keywords.
Rossi, Eino (Academic Press, 2014)We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. ...
Schultz, Timo (American Mathematical Society (AMS), 2021)In this paper, we prove that a metric measure space which has at least one open set isometric to an interval, and for which the (possibly non-unique) optimal transport map exists from any absolutely continuous measure to ...
Julia, Antoine; Nicolussi Golo, Sebastiano; Vittone, Davide (Springer Science and Business Media LLC, 2022)We consider submanifolds of sub-Riemannian Carnot groups with intrinsic C1 regularity (C1H). Our first main result is an area formula for C1H intrinsic graphs; as an application, we deduce density properties for Hausdorff ...
Käenmäki, Antti; Li, Bing (North-Holland, 2017)We prove that generically, for a self-affine set in Rd, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore ...
Käenmäki, Antti; Morris, Ian D. (Wiley-Blackwell Publishing Ltd., 2018)A fundamental problem in the dimension theory of self‐affine sets is the construction of high‐dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the set. A natural strategy for the construction ...