Now showing items 1-3 of 3

  • Dimension theory of random self-similar and self-affine constructions 

    Troscheit, Sascha (University of St Andrews, 2017-06-23) - Thesis
    This thesis is structured as follows. Chapter 1 introduces fractal sets before recalling basic mathematical concepts from dynamical systems, measure theory, dimension theory and probability theory. In Chapter 2 we give ...
  • Directed graph iterated function systems 

    Boore, Graeme C. (University of St Andrews, 2011-11-30) - Thesis
    This thesis concerns an active research area within fractal geometry. In the first part, in Chapters 2 and 3, for directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed ...
  • Self-affine sets with positive Lebesgue measure 

    Dajani, Karma; Jiang, Kan; Kempton, Thomas Michael William (2014-06-27) - Journal article
    Using techniques introduced by C. Gunturk, we prove that the attractors of a family of overlapping self-affine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds ...