University of Surrey

Test tubes in the lab Research in the ATI Dance Research

Dimensions of equilibrium measures on a class of planar self-affine sets

Fraser, Jonathan M, Jordan, Thomas and Jurga, Natalia (2018) Dimensions of equilibrium measures on a class of planar self-affine sets Journal of Fractal Geometry.

[img]
Preview
Text
fjj_final(1).pdf - Accepted version Manuscript

Download (312kB) | Preview

Abstract

We study equilibrium measures (K ̈aenm ̈aki measures) supported on self-affine sets generated by a finite collection of diagonal and anti-diagonal matrices acting on the plane and satisfying the strong separation property. Our main result is that such measures are exact dimensional and the dimension satisfies the Ledrappier-Young formula, which gives an explicit expression for the dimension in terms of the entropy and Lyapunov exponents as well as the dimension of a coordinate projection of the measure. In particular, we do this by showing that the K ̈aenm ̈aki measure is equal to the sum of (the pushforwards) of two Gibbs measures on an associated subshift of finite type.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Fraser, Jonathan M
Jordan, Thomas
Jurga, Natalian.jurga@surrey.ac.uk
Date : 2018
Copyright Disclaimer : Copyright 2018 European Mathematical Society
Uncontrolled Keywords : self-affine set, K ̈aenm ̈aki measure, quasi-Bernoulli mea- sure, exact dimensional, Ledrappier-Young formula
Depositing User : Melanie Hughes
Date Deposited : 20 Sep 2018 13:42
Last Modified : 19 Oct 2018 09:11
URI: http://epubs.surrey.ac.uk/id/eprint/849378

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year


Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800