Characterization of simple closed geodesics on Fricke surfaces

DOI10.1215/S0012-7094-85-05228-7zbMath0578.10027OpenAlexW1570927175MaRDI QIDQ1066177

Mark Sheingorn

Publication date: 1985

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-85-05228-7

Mathematics Subject Classification ID

Structure of modular groups and generalizations; arithmetic groups (11F06) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Homogeneous approximation to one number (11J04) Riemann surfaces (30F99)

Related Items

On the generalized Hurwitz equation and the Baragar-Umeda equation ⋮ Diophantine approximation on hyperbolic orbifolds ⋮ A variation of McShane's identity for 2-bridge links ⋮ Closed curves and geodesics with two self-intersections on the punctured torus ⋮ CLASSIFYING LOW HEIGHT GEODESICS ON $\Gamma^3 \backslash \mathcal{H}$ ⋮ LOW HEIGHT GEODESICS ON $\Gamma^3 \backslash \mathcal{H}$: HEIGHT FORMULAS AND EXAMPLES ⋮ McShane's identity, using elliptic elements ⋮ Closed Geodesics on a Riemann Surface With Application to the Markov Spectrum ⋮ Parametrizing simple closed geodesy on Γ³\ℋ

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The arithmetic and geometry of some hyperbolic three manifolds
• Diophantine approximation on hyperbolic Riemann surfaces
• Simple closed geodesics on 𝐻⁺/Γ(3) arise from the Markov spectrum
• Computing Self-Intersections of Closed Geodesics on Finite-Sheeted Covers of the Modular Surface
• Closed Geodesics on a Riemann Surface With Application to the Markov Spectrum
• On the Number of Markoff Numbers Below a Given Bound
• Minimum of quadratic forms with respect to Fuchsian groups. I.