Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727361 
Title:  Inhomogeneous Diophantine approximation, M_0 sets and projections of fractals  
Author:  Zafeiropoulos, Agamemnon 
ISNI:
0000 0004 6424 3319


Awarding Body:  University of York  
Current Institution:  University of York  
Date of Award:  2017  
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Abstract:  
The thesis deals with two main subjects, one being metric Diophantine approximation and the other Fractal Geometry. As far as the first subject is concerned, the results presented lie in the setup of inhomogeneous Diophantine approximation. The following is shown: suppose $\ca{A}=(q_n)_{n=1}^{\infty}\subseteq \mathbb{N}$ is a lacunary sequence and $\mu$ is a probability measure with Fourier transform of a prescribed logarithmic decay rate. Then for any $\gamma\in\mathbb{R}$ and any decreasing approximating function $\psi:\mathbb{N}\rightarrow \mathbb{R}^+$, the set $W_{\ca{A}}(\gamma,\psi)= \{x \in [0,1) : \q_nx  \gamma\ \leq \psi(q_n) \text{\ for i.m. } n\in\mathbb{N} \}$ satisfies a Khintchinetype law with respect to the measure $\mu$. This result builds on the work of Pollington and Velani. It is also shown that $W(\gamma,\psi)$ is a Salem set, generalising a result of Kaufman. Regarding Fractal Geometry, we present a refinement of Marstrand's famous projection theorem for arbitrary dimension functions. We state an analogue of Kaufman's result on the dimension of the set of angles of exceptional projections and discuss on the necessity of the conditions imposed in our main theorem.


Supervisor:  Velani, Sanju ; Zorin, Evgeniy  Sponsor:  Not available  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.727361  DOI:  Not available  
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