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Abstract
Previous study of the Assouad dimension of planar selfaffine 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 selfaffine 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 (selfsimilar) projection of the selfaffine 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 PrzytyckiUrbański sets to the lower local dimensions of Bernoulli convolutions.
Original language  English 

Pages (fromto)  49054918 
Journal  Proceedings of the American Mathematical Society 
Volume  145 
DOIs  
Publication status  Published  16 Jun 2017 
Keywords
 Assouad dimension
 Selfaffine carpet
 Local dimension
 Bernoulli
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Dive into the research topics of 'The Assouad dimension of selfaffine carpets with no grid structure'. Together they form a unique fingerprint.Projects
 1 Finished

Fractal Geometry and Dimension: Fractal Geometry and dimension theory
1/09/16 → 30/06/18
Project: Fellowship