Diophantine approximation on hyperbolic Riemann surfaces

DOI10.1007/BF02399200zbMath0593.10028MaRDI QIDQ1076063

Andrew Haas

Publication date: 1986

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

symbolic dynamicssimple geodesicshyperbolic surfacedepth of penetrationhyperbolic Riemann surfacesMarkov number

Mathematics Subject Classification ID

Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Homogeneous approximation to one number (11J04)

Related Items

The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms ⋮ On the Lenstra constant associated to the Rosen continued fractions ⋮ Diophantine approximation on hyperbolic orbifolds ⋮ THE GEOMETRY OF FAREY STAIRCASES ⋮ Systoles of arithmetic surfaces and Markoff spectrum ⋮ Self-intersections of curves on surfaces ⋮ Markov spectra for modular billiards ⋮ On the Lagrange and Markov dynamical spectra for geodesic flows on surfaces with negative curvature ⋮ CLASSIFYING LOW HEIGHT GEODESICS ON $\Gamma^3 \backslash \mathcal{H}$ ⋮ McShane's identity, using elliptic elements ⋮ Persistent Hall rays for Lagrange spectra at cusps of Riemann surfaces ⋮ Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space ⋮ The sum of Lagrange numbers ⋮ Spiraling spectra of geodesic lines in negatively curved manifolds ⋮ Statistical mechanics of \(2+1\) gravity from Riemann zeta function and Alexander polynomial: Exact results ⋮ Markov numbers, Mather’s β function and stable norm ⋮ The distribution of geodesic excursions out the end of a hyperbolic orbifold and approximation with respect to a Fuchsian group ⋮ Closed Geodesics on a Riemann Surface With Application to the Markov Spectrum ⋮ Unnamed Item ⋮ Parametrizing simple closed geodesy on Γ³\ℋ ⋮ Conway topograph, -dynamics and two-valued groups ⋮ The modular torus has maximal length spectrum ⋮ The Markov spectra for Fuchsian groups ⋮ Geometry and Markoff’s spectrum for ℚ(𝕚), I ⋮ Combinatorial growth in the modular group ⋮ Characterization of simple closed geodesics on Fricke surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics
• Foliations and laminations on hyperbolic surfaces
• Length spectra as moduli for hyperbolic surfaces
• On free Kleinian groups
• Limit points of Kleinian groups and finite sided fundamental polyhedra
• Simple closed geodesics on 𝐻⁺/Γ(3) arise from the Markov spectrum
• Diophantine Approximation and Horocyclic Groups
• The infinite word problem and limit sets in Fuchsian groups
• Minimum of quadratic forms with respect to Fuchsian groups. I.
• An Algorithm for Simple Curves on Surfaces
• Representation of Markoff's binary quadratic forms by geodesics on a perforated torus