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 PrzytyckiUrba\'nski sets to the lower local dimensions of Bernoulli convolutions.
Original language  English 

Pages (fromto)  49054918 
Number of pages  14 
Journal  Proceedings of the American Mathematical Society 
Volume  145 
Issue number  11 
Early online date  16 Jun 2017 
DOIs  
Publication status  Published  1 Nov 2017 
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Dr Thomas M Jordan
 Probability, Analysis and Dynamics
 School of Mathematics  Senior Lecturer in Pure Mathematics
 Pure Mathematics
 Ergodic theory and dynamical systems
Person: Academic , Member