Farey polytopes and continued fractions associated with discrete hyperbolic groups

DOI10.1090/S0002-9947-99-02151-0zbMath0924.11061OpenAlexW1553426976MaRDI QIDQ4243603

L. Ya. Vulakh

Publication date: 19 May 1999

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02151-0

zbMATH Keywords

Clifford algebrascontinued fractionsdiophantine approximationhyperbolic geometryspectral approximationFarey tessellationsHurwitz approximation constant

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Homogeneous approximation to one number (11J04) Diophantine approximation, transcendental number theory (11J99)

Related Items (15)

The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms ⋮ Orientation preserving Möbius transformations in \(\mathbb{R}_\infty^4\) and quaternionic determinants ⋮ DIOPHANTINE APPROXIMATION IN $\mathbf{Q}(\sqrt{-5})$ AND $\mathbf{Q}(\sqrt{-6})$ ⋮ The geometry of Gaussian integer continued fractions ⋮ Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds ⋮ Geodesic Gaussian integer continued fractions ⋮ Diophantine approximation in \(\mathbb{Q}(\sqrt{-30})\), \(\mathbb{Q}(\sqrt{-33})\) and \(\mathbb{Q}(\sqrt{-57})\) ⋮ The Farey octahedron graph, the Poincaré polyhedron theorem and Gaussian integer continued fractions ⋮ HERMITIAN POINTS IN MARKOV SPECTRA ⋮ DIOPHANTINE APPROXIMATION IN IMAGINARY QUADRATIC FIELDS ⋮ Reduction theory over quadratic imaginary fields ⋮ THE MARKOV SPECTRA FOR COCOMPACT FUCHSIAN GROUPS ⋮ Units in some families of algebraic number fields ⋮ The Markov spectra for Fuchsian groups ⋮ Lagrange spectra in Teichmüller dynamics via renormalization

Cites Work

• 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
• Diophantine approximation in the Eisensteinian field
• Polyhedral groups and graph amalgamation products
• Komplex-quadratische Zahlkörper kleiner Diskriminante und Pflasterungen des dreidimensionalen Hyperbolischen Raumes
• Diophantine approximation of complex numbers
• Diophantine approximation in the field \(\mathbb{Q}(i(11^{1/2}))\)
• Limit points of Kleinian groups and finite sided fundamental polyhedra
• Diophantine approximation on Bianchi groups
• Generators and relations for certain special linear groups
• On the Markov spectrum for the imaginary quadratic fields \(Q(i \sqrt D)\), where \(D \not \equiv 3\) (mod 4)
• A class of continued fractions associated with certain properly discontinuous groups
• The Modular Surface and Continued Fractions
• The Hurwitz Constant and Diophantine Approximation on Hecke Groups
• Higher Dimensional Analogues of the Modular and Picard Groups
• Diophantine Approximation in R n
• On Hurwitz Constants for Fuchsian Groups
• Farey Triangles and Farey Quadrangels in the Complex Plane.
• Farey Simplices in the Space of Quaternions.

This page was built for publication: Farey polytopes and continued fractions associated with discrete hyperbolic groups