Now showing items 1-7 of 7

    • Dimension growth for iterated sumsets 

      Fraser, Jonathan; Howroyd, Douglas Charles; Yu, Han (2018-12-17) - Journal article
      We study dimensions of sumsets and iterated sumsets and provide natural conditions which guarantee that a set F⊆ℝ satisfies ^dim^BF+F>^dim^BF or even dimHnF→1. Our results apply to, for example, all uniformly perfect sets, ...
    • Dimension theory and fractal constructions based on self-affine carpets 

      Fraser, Jonathan M. (University of St Andrews, 2013-11-29) - Thesis
      The aim of this thesis is to develop the dimension theory of self-affine carpets in several directions. Self-affine carpets are an important class of planar self-affine sets which have received a great deal of attention ...
    • Inhomogeneous self-similar sets and measures 

      Snigireva, Nina (University of St Andrews, 2008) - Thesis
      The thesis consists of four main chapters. The first chapter includes an introduction to inhomogeneous self-similar sets and measures. In particular, we show that these sets and measures are natural generalizations of ...
    • Inhomogeneous self-similar sets with overlaps 

      Baker, Simon; Fraser, Jonathan M.; Máthé, András (2019-01) - Journal article
      It is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of the upper box dimensions of the homogeneous ...
    • On average Hewitt-Stromberg measures of typical compact metric spaces 

      Olsen, Lars (2019-01-24) - Journal article
      We study average Hewitt-Stromberg measures of typical compact metric spaces belonging to the Gromov-Hausdorff space (of all compact metric spaces) equipped with the Gromov-Hausdorff metric.
    • On the Hausdorff and packing measures of typical compact metric spaces 

      Jurina, S.; MacGregor, N.; Mitchell, A.; Olsen, L.; Stylianou, A. (2018-08) - Journal article
      We study the Hausdorff and packing measures of typical compact metric spaces belonging to the Gromov–Hausdorff space (of all compact metric spaces) equipped with the Gromov–Hausdorff metric.
    • Quantifying inhomogeneity in fractal sets 

      Fraser, Jonathan; Todd, Michael John (2018-04) - Journal article
      An inhomogeneous fractal set is one which exhibits different scaling behaviour at different points. The Assouad dimension of a set is a quantity which finds the ‘most difficult location and scale’ at which to cover the set ...