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Title: Dimension theory and dynamically defined sets
Author: Ferguson, Andrew J.
ISNI:       0000 0004 2748 4228
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2011
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The first topic of this thesis is concerned with the application of the continuous perturbation theory of Keller and Liverani to investigate the statistical properties of dynamical systems with holes. The main result of Chapter 3 is a perturbation result for a singularly perturbed transfer operator in the setting of subshifts of finite type. Chapter 4 investigates the consequences of this result for an expanding map of a compact metric space. In this chapter results laws concerning escape rates, extreme value theory, Hausdorff dimension and return time statistics are derived. The second main component of the thesis is the study of the orthogonal projection of dynamically defined sets in the plane. In Chapter 5 we build on the work of Peres and Shmerkin, proving that if an irrationality condition holds for certain classes of dynamically defined planar sets then the exceptional set of directions in Marstrand’s theorem can be computed explicitly.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics