Geodesic
Properties of quasi-Assouad dimension
Ignacio García1 ; Kathryn Hare2
1Universidad 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)
2University 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/