Fractal geometry of the complement of Lagrange spectrum in Markov spectrum

DOI10.4171/CMH/498zbMath1465.11165arXiv1803.01230OpenAlexW3179013812MaRDI QIDQ2214033

Carlos Matheus, Carlos Gustavo T.de A. Moreira

Publication date: 4 December 2020

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.01230

zbMATH Keywords

Hausdorff dimensionMarkov and Lagrange spectraCusick's conjecture

Mathematics Subject Classification ID

Dynamical systems with hyperbolic orbits and sets (37D05) Dynamical systems involving maps of the interval (37E05) Markov and Lagrange spectra and generalizations (11J06)

Related Items (5)

Corrigendum and addendum to: ``Fractal geometry of the complement of Lagrange spectrum in Markov spectrum ⋮ Non-planarity of Markoff graphs \(\mod p\) ⋮ Hausdorff dimension of Gauss-Cantor sets and two applications to classical Lagrange and Markov spectra ⋮ Unnamed Item ⋮ Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups

Cites Work

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• The connection between the Lagrange and Markoff spectra
• Accumulation points of the Lagrange and Markov spectra
• Geometric properties of the Markov and Lagrange spectra
• Rigorous effective bounds on the Hausdorff dimension of continued fraction Cantor sets: A hundred decimal digits for the dimension of \(E_{2}\)
• Markov spectrum near Freiman's isolated points in \(M\setminus L\)
• A polynomial time algorithm for the Hausdorff dimension of continued fraction Cantor sets
• Noncoincidence of the Markov and Lagrange spectra
• On the sum and product of continued fractions
• Computing the dimension of dynamically defined sets: E_2 and bounded continued fractions
• ${\rm HD}(M\setminus L) > 0.353$

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