Now showing items 1-9 of 9

  • 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 ...
  • Hitting times and periodicity in random dynamics 

    Todd, Michael John; Rousseau, Jerome (2015-10) - Journal article
    We prove quenched laws of hitting time statistics for random subshifts of finite type. In particular we prove a dichotomy between the law for periodic and for non-periodic points. We show that this applies to random Gibbs ...
  • Linear response for intermittent maps 

    Baladi, Viviane; Todd, Michael John (2016-11) - Journal article
    We consider the one parameter family α↦Tα (α∈[0,1)) of Pomeau-Manneville type interval maps Tα(x)=x(1+2αxα) for x∈[0,1/2) and Tα(x)=2x−1 for x∈[1/2,1], with the associated absolutely continuous invariant probability measure ...
  • Multifractal zeta functions 

    Mijović, Vuksan (University of St Andrews, 2017-06-23) - Thesis
    Multifractals have during the past 20 − 25 years been the focus of enormous attention in the mathematical literature. Loosely speaking there are two main ingredients in multifractal analysis: the multifractal spectra and ...
  • Recurrence and transience for suspension flows 

    Iommi, Godofredo; Jordan, Thomas; Todd, Michael John (2015) - Journal article
    We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium ...
  • Recurrence statistics for the space of interval exchange maps and the Teichmüller flow on the space of translation surfaces 

    Aimino, Romain; Nicol, Matthew; Todd, Michael John (2017-08) - Journal article
    In this paper we show that the transfer operator of a Rauzy–Veech–Zorich renormalization map acting on a space of quasi-Hölder functions is quasicompact and derive certain statistical recurrence properties for this map and ...
  • Speed of convergence for laws of rare events and escape rates 

    Freitas, Ana; Freitas, Jorge; Todd, Michael John (2015-04) - Journal article
    We obtain error terms on the rate of convergence to Extreme Value Laws, and to the asymptotic Hitting Time Statistics, for a general class of weakly dependent stochastic processes. The dependence of the error terms on the ...
  • Transience and multifractal analysis 

    Iommi, Godofredo; Jordan, Thomas; Todd, Michael John (2016-01-11) - 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 ...
  • Wild attractors and thermodynamic formalism 

    Bruin, Henk; Todd, Michael John (2015-09) - Journal article
    Fibonacci unimodal maps can have a wild Cantor attractor, and hence be Lebesgue dissipative, depending on the order of the critical point. We present a one-parameter family ƒλ of countably piecewise linear unimodal Fibonacci ...