Properties of quasi-Assouad dimension

Kirjoittajat

  • Ignacio García 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)
  • Kathryn Hare University of Waterloo, Department of Pure Mathematics

Avainsanat:

Assouad dimension, weak tangents, orthogonal projections

Abstrakti

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.

 

Osasto
Articles

Julkaistu

2021-06-21

Viittaaminen

García, I., & Hare, K. (2021). Properties of quasi-Assouad dimension. Annales Fennici Mathematici, 46(1), 279–293. Noudettu osoitteesta https://afm.journal.fi/article/view/109582