The Assouad dimension of self-affine carpets with no grid structure

Jonathan M. Fraser; Thomas Jordan

doi:10.1090/proc/13629

The Assouad dimension of self-affine carpets with no grid structure

Jonathan M. Fraser, Thomas Jordan

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Previous study of the Assouad dimension of planar self-affine sets has relied heavily on the underlying IFS having a `grid structure', thus allowing for the use of approximate squares. We study the Assouad dimension of a class of self-affine carpets which do not have an associated grid structure. We find that the Assouad dimension is related to the box and Assouad dimensions of the (self-similar) projection of the self-affine set onto the first coordinate and to the local dimensions of the projection of a natural Bernoulli measure onto the first coordinate. In a special case we relate the Assouad dimension of the Przytycki-Urbański sets to the lower local dimensions of Bernoulli convolutions.

Original language	English
Pages (from-to)	4905-4918
Journal	Proceedings of the American Mathematical Society
Volume	145
DOIs	https://doi.org/10.1090/proc/13629
Publication status	Published - 16 Jun 2017

Keywords

Assouad dimension
Self-affine carpet
Local dimension
Bernoulli

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10.1090/proc/13629

Fraser_2016_Assouad_nogrig_PAMS_AAM
© 2017, American Mathematical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1090/proc/13629
Accepted author manuscript, 287 KB

Fractal Geometry and Dimension: Fractal Geometry and dimension theory
Fraser, J. (PI)
The Leverhulme Trust
1/09/16 → 30/06/18
Project: Fellowship

Cite this

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abstract = "Previous study of the Assouad dimension of planar self-affine sets has relied heavily on the underlying IFS having a `grid structure', thus allowing for the use of approximate squares. We study the Assouad dimension of a class of self-affine carpets which do not have an associated grid structure. We find that the Assouad dimension is related to the box and Assouad dimensions of the (self-similar) projection of the self-affine set onto the first coordinate and to the local dimensions of the projection of a natural Bernoulli measure onto the first coordinate. In a special case we relate the Assouad dimension of the Przytycki-Urba{\'n}ski sets to the lower local dimensions of Bernoulli convolutions.",

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ER -

The Assouad dimension of self-affine carpets with no grid structure

Abstract

Keywords

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Fractal Geometry and Dimension: Fractal Geometry and dimension theory

Cite this