Parametrizing simple closed geodesy on Γ3\ℋ

DOI10.1017/S1446788700003116zbMath1111.11035OpenAlexW2129484829MaRDI QIDQ4709355

Thomas A. Schmidt, Mark Sheingorn

Publication date: 22 June 2003

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788700003116

zbMATH Keywords

alignmentTeichmüller spaceautomorphismsliftslaminationsMöbius transformationelliptic fixed pointgeodesic arcstrain trackslabyrinthMarkoff equationpunctured toribasic arc parametrizationcanonical geometric pairing of simple closed curvesdegree three cover of the modular surfaceisometry classes of predetermined lengthMar\-koff triplespaths and words of simple closed geodesicsproper single self-intersecting geodesies of Crisp and Morantine pa\-ra\-met\-ri\-za\-tiontine signatures

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Markov and Lagrange spectra and generalizations (11J06) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (4)

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 ⋮ Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space

Cites Work

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• The geometry of Markoff numbers
• Characterization of simple closed geodesics on Fricke surfaces
• Diophantine approximation on hyperbolic Riemann surfaces
• Diophantine approximation on hyperbolic orbifolds
• Simple geodesics and a series constant over Teichmüller space
• Approach to Markoff's minimal forms through modular functions
• Simple closed geodesics on 𝐻⁺/Γ(3) arise from the Markov spectrum
• Combinatorics of Train Tracks. (AM-125)

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