Geodesic
Properties of quasi-Assouad dimension
Ignacio García1 ; Kathryn Hare2
1 Universidad Nacional de Mar del Plata, Facultad de Ciencias Exactas y Naturales, Instituto de Investigaciones Físicas de Mar del Plata (CONICET), Centro Marplatense de Investigaciones Matemáticas (CIC)
2 University of Waterloo, Department of Pure Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 279-293

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The connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of the quasi-Assouad dimension for a class of planar self-affine sets. We also show that sets with decreasing gaps have quasi-Assouad dimension 0 or 1 and exhibit an example of a set in the plane whose quasi-Assouad dimension is smaller than that of its projection onto the $x$-axis, showing that quasi-Assouad dimension may increase under Lipschitz mappings. Moreover, for closed sets, we show that the Hausdorff dimension is an upper bound for the quasi-lower Assouad dimension.  
Keywords: Assouad dimension, weak tangents, orthogonal projections

Ignacio García 1 ; Kathryn Hare 2

1 Universidad Nacional de Mar del Plata, Facultad de Ciencias Exactas y Naturales, Instituto de Investigaciones Físicas de Mar del Plata (CONICET), Centro Marplatense de Investigaciones Matemáticas (CIC)
2 University of Waterloo, Department of Pure Mathematics 
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Ignacio García; Kathryn Hare. Properties of quasi-Assouad dimension. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 279-293. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a14/