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

DOI10.1090/btran/109OpenAlexW3111526499MaRDI QIDQ5872965

Mark Pollicott, Polina Vytnova

Publication date: 5 January 2023

Published in: Transactions of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.07083

zbMATH Keywords

Hausdorff dimensionlimit setsZaremba conjectureLagrange and Markov spectraMarkov iterated function schemes

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Markov and Lagrange spectra and generalizations (11J06) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (4)

Non-commutative methods in additive combinatorics and number theory ⋮ Lower bounds on the Hausdorff dimension of some Julia sets ⋮ Modular generalization of the Bourgain-Kontorovich theorem ⋮ Hausdorff dimension of Gauss-Cantor sets and two applications to classical Lagrange and Markov spectra

Uses Software

• Arb

Cites Work

• The thermodynamic formalism for expanding maps
• Hausdorff dimension of quasi-circles
• Continued fraction Cantor sets, Hausdorff dimension, and functional analysis
• \(C^m\) eigenfunctions of Perron-Frobenius operators and a new approach to numerical computation of Hausdorff dimension: applications in \(\mathbb R^1\)
• Spectral Galerkin methods for transfer operators in uniformly expanding dynamics
• Perturbation theory for linear operators.
• Related aspects of positivity in Riemannian geometry
• On the dimension of deterministic and random Cantor-like sets
• A polynomial time algorithm for the Hausdorff dimension of continued fraction Cantor sets
• Hidden positivity and a new approach to numerical computation of Hausdorff dimension: higher order methods
• Fractal geometry of the complement of Lagrange spectrum in Markov spectrum
• On a modular form of Zaremba's conjecture
• A strengthening of a theorem of Bourgain-Kontorovich. II
• Uniform congruence counting for Schottky semigroups in \(\mathrm{SL}_2(\mathbb{Z})\)
• Rigorous high-precision computation of the Hurwitz zeta function and its derivatives
• An improvement to Zaremba's conjecture
• A strengthening of a theorem of Bourgain and Kontorovich. V
• On the sum and product of continued fractions
• Asymmetric minima of quadratic forms and asymmetric Diophantine approximation
• A strengthening of a theorem of Bourgain and Kontorovich. IV
• Rigorous dimension estimates for Cantor sets arising in Zaremba theory
• Hausdorff dimension and conformal dynamics, III: Computation of dimension
• Calculating Hausdorff dimension of Julia sets and Kleinian limit sets
• Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic
• Repellers for real analytic maps
• On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces
• Thermodynamic Formalism
• From Apollonius to Zaremba: Local-global phenomena in thin orbits
• DYNAMICAL SYSTEMS, FRACTAL GEOMETRY AND DIOPHANTINE APPROXIMATIONS
• On the dimension spectrum of infinite subsystems of continued fractions
• Is Zaremba's conjecture true?
• A strengthening of a theorem of Bourgain and Kontorovich
• ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE
• On Zaremba's conjecture
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Hausdorff dimension estimates applied to Lagrange and Markov spectra, Zaremba theory, and limit sets of Fuchsian groups