Dimensions of equilibrium measures on a class of planar self-affine sets
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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.
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Official URL: https://www.ems-ph.org/journals/all_issues.php?iss...
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 | ||||||||||||
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| Divisions : | Faculty of Engineering and Physical Sciences > Mathematics | ||||||||||||
| Authors : |
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| 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 |
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