Now showing items 1-14 of 14

    • Assouad type dimensions and homogeneity of fractals 

      Fraser, Jonathan M. (2014-12) - Journal article
      We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural 'dimension pair'. In particular, we compute these dimensions for certain classes of self-affine sets and ...
    • Dimension and measure for generic continuous images 

      Balka, Richard; Farkas, Abel; Fraser, Jonathan M.; Hyde, James T. (2013) - Journal article
      We consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, X, into R-n. The key question is 'what is the generic dimension of f(X)?' and we consider two different ...
    • Dimension and measure theory of self-similar structures with no separation condition 

      Farkas, Ábel (University of St Andrews, 2015-11-30) - Thesis
      We introduce methods to cope with self-similar sets when we do not assume any separation condition. For a self-similar set K ⊆ ℝᵈ we establish a similarity dimension-like formula for Hausdorff dimension regardless of any ...
    • 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 ...
    • Multifractal spectra and multifractal zeta-functions 

      Mijovic, Vuksan; Olsen, Lars Ole Ronnow (2017-02) - Journal article
      We introduce multifractal zetafunctions providing precise information of a very general class of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra ...
    • On simultaneous local dimension functions of subsets of Rd 

      Olsen, Lars Ole Ronnow (2015-09-30) - Journal article
      For a subset E ⊑ Rd and x ∈ Rd, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by (Formula presented.) where dimH and dimP denote the Hausdorff dimension and ...
    • On the Hausdorff dimension of microsets 

      Fraser, Jonathan MacDonald; Howroyd, Douglas Charles; Käenmäki, Antti; Yu, Han (2019-06-10) - Journal article
      We investigate how the Hausdorff dimensions of microsets are related to the dimensions of the original set. It is known that the maximal dimension of a microset is the Assouad dimension of the set. We prove that the lower ...
    • On the Lq -spectrum of planar self-affine measures 

      Fraser, Jonathan M. (2016) - Journal article
      We study the dimension theory of a class of planar self-affine multifractal measures. These measures are the Bernoulli measures supported on box-like self-affine sets, introduced by the author, which are the attractors of ...
    • Resonances for graph directed Markov systems, and geometry of infinitely generated dynamical systems 

      Hille, Martial R. (University of St Andrews, 2009-06-24) - Thesis
      In the first part of this thesis we transfer a result of Guillopé et al. concerning the number of zeros of the Selberg zeta function for convex cocompact Schottky groups to the setting of certain types of graph ...
    • Some results in support of the Kakeya conjecture 

      Fraser, Jonathan MacDonald; Olson, Eric; Robinson, James (2017-10-01) - Journal article
      A Besicovitch set is a subset of Rd that contains a unit line segment in every direction and the famous Kakeya conjecture states that Besicovitch sets should have full dimension. We provide a number of results in support ...
    • Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes 

      Falconer, Kenneth; Mattila, Pertti (2016) - Journal article
      We present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s-dimensional Hausdorff measure, there is a set X of directions of Lebesgue ...
    • A uniform dimension result for two-dimensional fractional multiplicative processes 

      Jin, Xiong (2014-03) - Journal article
      We show that a two-dimensional fractional multiplicative process has a uniform Hausdorff dimension result if and only if the two parameters of the process coincide.