Ledrappier–Young formulae for a family of nonlinear attractors
Date
04/10/2021Keywords
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Abstract
We study a natural class of invariant measures supported on the attractors of a family of nonlinear, non-conformal iterated function systems introduced by Falconer, Fraser and Lee. These are pushforward quasi-Bernoulli measures, a class which includes the well-known class of Gibbs measures for Hölder continuous potentials. We show that these measures are exact dimensional and that their exact dimensions satisfy a Ledrappier–Young formula.
Citation
Lee , L D & Jurga , N A 2021 , ' Ledrappier–Young formulae for a family of nonlinear attractors ' , Mathematische Zeitschrift , vol. First Online . https://doi.org/10.1007/s00209-021-02876-7
Publication
Mathematische Zeitschrift
Status
Peer reviewed
ISSN
0025-5874Type
Journal article
Rights
Copyright © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Description
LDL was supported by an EPSRC Doctoral Training Grant (EP/N509759/1). NJ was supported by an EPSRC Standard Grant (EP/R015104/1).Collections
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