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Equilibrium states of generalised singular value potentials and applications to affine iterated function systems

Bochi, Jairo and Morris, Ian D. (2018) Equilibrium states of generalised singular value potentials and applications to affine iterated function systems Geometric And Functional Analysis.

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Abstract

We completely describe the equilibrium states of a class of potentials over the full shift which includes Falconer's singular value function for affine iterated function systems with invertible affinities. We show that the number of distinct ergodic equilibrium states of such a potential is bounded by a number depending only on the dimension, answering a question of A. Käenmäki. We prove that all such equilibrium states are fully supported and satisfy a Gibbs inequality with respect to a suitable subadditive potential. We apply these results to demonstrate that the affinity dimension of an iterated function system with invertible affinities is always strictly reduced when any one of the maps is removed, resolving a folklore open problem in the dimension theory of self-affine fractals. We deduce a natural criterion under which the Hausdorff dimension of the attractor has the same strict reduction property.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Bochi, Jairo
Morris, Ian D.i.morris@surrey.ac.uk
Date : 2018
Copyright Disclaimer : Copyright 2018 Springer Verlag.
Depositing User : Clive Harris
Date Deposited : 23 Mar 2018 09:20
Last Modified : 23 Mar 2018 09:20
URI: http://epubs.surrey.ac.uk/id/eprint/846070

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