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Some observations on Käenmäki measures

Morris, Ian (2018) Some observations on Käenmäki measures Annales Academiæ Scientiarum Fennicæ, 43. pp. 945-960.

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In this note we investigate some properties of equilibrium states of affine iterated function systems, sometimes known as Kaenmaki measures. We give a simple sufficient condition for Kaenmaki measures to have a gap between certain specific pairs of Lyapunov exponents, partially answering a question of B. Barany, A. Kaenmaki and H. Koivusalo. We also give sharp bounds for the number of ergodic Kaenmaki measures in dimensions up to 4, answering a question of J. Bochi and the author within this range of dimensions. Finally, we pose an open problem on the Hausdorff dimension of self-affine measures which may be reduced to a statement concerning semigroups of matrices in which a particular weighted product of absolute eigenvalues is constant.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 2018
DOI : 10.5186/aasfm.2018.4357
Copyright Disclaimer : Copyright © 2018 by Academia Scientiarum Fennica. Reproduced here by kind permission of the publishers.
Depositing User : Melanie Hughes
Date Deposited : 17 Apr 2018 11:10
Last Modified : 05 Nov 2018 14:10

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