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Abstract
We study equilibrium measures (Käenmäki 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 Käenmäki measure is equal to the sum of (the pushforwards) of two Gibbs measures on an associated subshift of finite type.
Original language | English |
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Pages (from-to) | 87–111 |
Journal | Journal of Fractal Geometry |
Volume | 7 |
Issue number | 1 |
Early online date | 13 Nov 2019 |
DOIs | |
Publication status | Published - 2020 |
Keywords
- Self-affine set
- Käenmäki measure
- Quasi-Bernoulli measure
- Exact dimensional
- Ledrappier-Young formula
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Dive into the research topics of 'Dimensions of equilibrium measures on a class of planar self-affine sets'. Together they form a unique fingerprint.Projects
- 1 Finished
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Fractal Geometry and Dimension: Fractal Geometry and dimension theory
Fraser, J. (PI)
1/09/16 → 30/06/18
Project: Fellowship