Browsing by Name "Todd, Michael John"
Now showing items 1-10 of 10
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Dimension theory of random self-similar and self-affine constructions
(University of St Andrews, 2017-06-23) - ThesisThis 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
(2015-10) - Journal articleWe 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
(2016-11) - Journal articleWe 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
(University of St Andrews, 2017-06-23) - ThesisMultifractals 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
(2015) - Journal articleWe 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
(2017-08) - Journal articleIn 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 ... -
Return times at periodic points in random dynamics
(2017-01) - Journal articleWe prove a quenched limiting law for random measures on subshifts at periodic points. We consider a family of measures {µω}ω∈Ω, where the ‘driving space’ Ω is equipped with a probability measure which is invariant under a ... -
Speed of convergence for laws of rare events and escape rates
(2015-04) - Journal articleWe 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
(2017-03) - Journal articleWe 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
(2015-09) - Journal articleFibonacci 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 ...