On numbers badly approximable by q-adic rationals

Research output: ThesisDoctoral Thesis (monograph)

Abstract

The thesis takes as starting point diophantine approximation with focus on the area of badly approximable numbers. For the special kind of rationals, the q-adic rationals, we consider two types of approimations models, a one-sided and a two-sided model, and the sets of badly approximable numbers they give rise to. We prove with elementary methods that the Hausdorff dimension of these two sets depends continuously on a defining parameter, is constant Lebesgue almost every and self similar. Hence they are fractal sets. Moreover, we give the complete description of the intervals where the dimension remains unchanged. The methods and techniques in the proofs uses ideas form symbolic dynamics, combinatorics on words and the beta-shift.

Details

Authors
  • Johan Nilsson
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Number theory, Symbolic dynamics, Combinatorics on words, Badly approximable numbers, Diophantine approximation, Mathematics, Matematik, Dynamical systems
Original languageEnglish
QualificationDoctor
Awarding Institution
Supervisors/Assistant supervisor
  • Schmeling, Jörg and Vaienti, Sandro, Schmeling, Jörg and Vaienti, Sandro, Supervisor, External person
Award date2007 Dec 6
Publisher
  • Centre for Mathematical Sciences, Lund University
Print ISBNs978-91-628-7334-9
Publication statusPublished - 2007
Publication categoryResearch

Bibliographic note

Defence details Date: 2007-12-06 Time: 13:15 Place: Lecture room MH:C, Centre for mathematical sciences, Sölvegatan 18, Lund University Faculty of Engineering External reviewer(s) Name: Bugeaud, Yann Title: Professor Affiliation: Université Louis Pasteur, Mathématique, Strasbourg, France ---