On the dimension of planar self-affine sets with non-invertible maps

Balázs Bárány; Viktor Körtvélyesi

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arXiv · 2302.13037

On the dimension of planar self-affine sets with non-invertible maps

Balázs Bárány·Viktor Körtvélyesi

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Abstract

In this paper, we study the dimension of planar self-affine sets, of which generating iterated function system (IFS) contains non-invertible affine mappings. We show that under a certain separation condition, the dimension equals to the affinity dimension for a typical choice of the linear parts of the non-invertible mappings, furthermore, we show that the dimension is strictly smaller than the affinity dimension for certain choices of parameters.

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BibTeX RIS

Balázs Bárány, Viktor Körtvélyesi. 2023-07-31. On the dimension of planar self-affine sets with non-invertible maps. https://arxiv.org/abs/2302.13037

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