Now showing items 1-6 of 6

    • Bernoulli convolutions and 1D dynamics 

      Kempton, Thomas Michael William; Persson, Tomas (2015-10-08) - Journal article
      We describe a family φλ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding ...
    • A commutative noncommutative fractal geometry 

      Samuel, Anthony (University of St Andrews, 2010) - Thesis
      In this thesis examples of spectral triples, which represent fractal sets, are examined and new insights into their noncommutative geometries are obtained. Firstly, starting with Connes' spectral triple for a non-empty ...
    • Digit frequencies and Bernoulli convolutions 

      Kempton, Thomas Michael William (2014-06-27) - Journal article
      It is well known that when β is a Pisot number, the corresponding Bernoulli convolution ν(β) has Hausdorff dimension less than 1, i.e. that there exists a set A(β) with (ν(β))(A(β))=1 and dim_H(A(β))<1. We show explicitly ...
    • Finite and infinite ergodic theory for linear and conformal dynamical systems 

      Munday, Sara (University of St Andrews, 2011-11-30) - Thesis
      The first main topic of this thesis is the thorough analysis of two families of piecewise linear maps on the unit interval, the α-Lüroth and α-Farey maps. Here, α denotes a countably infinite partition of the unit interval ...
    • 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 ...
    • Transience and multifractal analysis 

      Iommi, Godofredo; Jordan, Thomas; Todd, Michael John (2017-03) - Journal article
      We study dimension theory for dissipative dynamical systems, proving a conditional variational principle for the quotients of Birkhoff averages restricted to the recurrent part of the system. On the other hand, we show ...