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Corpus ID: 229153115

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

@article{Pollicott2020HausdorffDE,
title={Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups},
author={M. Pollicott and P. Vytnova},
journal={arXiv: Dynamical Systems},
year={2020}
}

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. As our first application we confirm, and often strengthen, conjectures on the difference of the… Expand