On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems.(English)Zbl 1406.28005
The authors prove, under mild technical conditions, that the affinity dimension of a planar self-affine set is equal to the supremum of the Lyapunov dimensions of self-affine measures supported by self-affine proper subsets of the original set. Moreover, the above-mentioned self-affine subsets may be chosen so as to have stronger separation properties and in such a way that the linear parts of their affinities are positive matrices. In particular, they obtain new criteria under which the Hausdorff dimension of a self-affine set equals its affinity dimension.
Reviewer: George Stoica (Saint John)
MSC:
| 28A80 | Fractals |
| 37C45 | Dimension theory of smooth dynamical systems |
| 37D35 | Thermodynamic formalism, variational principles, equilibrium states for dynamical systems |
Cite
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