Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups

13 Dec 2020 Mark Pollicott Polina Vytnova

In this note we will describe a simple and practical approach to get rigorous bounds on the Hausdorff dimension of limits sets for some one dimensional Markov iterated function schemes. The general problem has attracted considerable attention, but we are particularly concerned with the role of the value of the Hausdorff dimension in solving conjectures and problems in other areas red of mathematics... (read more)

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Categories


  • DYNAMICAL SYSTEMS
  • NUMBER THEORY
  • 37C30, 37D35, 11K55, 11J06