On the construction of the natural extension of the Hurwitz complex continued fraction map

DOI10.1007/s00605-018-1229-0zbMath1414.11090OpenAlexW2899904828WikidataQ128953192 ScholiaQ128953192MaRDI QIDQ1757399

Rie Natsui, Hitoshi Nakada, Shunji Ito, Hiromi Ei

Publication date: 4 January 2019

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-018-1229-0

zbMATH Keywords

invariant measuretilingnatural extensioncomplex continued fractions

Mathematics Subject Classification ID

Combinatorial aspects of tessellation and tiling problems (05B45) Metric theory of continued fractions (11K50) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (11)

Sets of exact approximation order by complex rational numbers ⋮ Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics ⋮ Calculations of the Invariant Measure for Hurwitz Continued Fractions ⋮ On the existence of the Legendre constants for some complex continued fraction expansions over imaginary quadratic fields ⋮ On the ergodic theory of maps associated with the nearest integer complex continued fractions over imaginary quadratic fields ⋮ On sums of partial quotients in Hurwitz continued fraction expansions ⋮ On the Legendre and the Lenstra constants for complex continued fractions introduced by J. Hurwitz ⋮ Alternating $N$-expansions ⋮ A complex Borel-Bernstein theorem ⋮ Finite Partitions for Several Complex Continued Fraction Algorithms ⋮ THE DIFFERENCE BETWEEN THE HURWITZ CONTINUED FRACTION EXPANSIONS OF A COMPLEX NUMBER AND ITS RATIONAL APPROXIMATIONS

Cites Work

• On the Lenstra constant associated to the Rosen continued fractions
• A complex continued fraction transformation and its ergodic properties
• On ergodic theory of A. Schmidt's complex continued fractions over Gaussian field
• Ergodic theory for complex continued fractions
• Approximation properties of some complex continued fractions
• Diophantine approximation of complex numbers
• On the metrical theory of continued fraction mixing fibred systems and its application to Jacobi-Perron algorithm
• Multi-dimensional maps with infinite invariant measures and countable state sofic shifts
• A continued fraction proof of Ford's theorem on complex rational approximations.
• Shorter Notes: Continued Fractions and Equivalent Complex Numbers
• Kuzmin's theorem revisited
• Continued fractions for complex numbers and values of binary quadratic forms
• Some ergodic properties of multi-dimensional f-expansions
• Disk-like self-affine tiles in \(\mathbb{R}^2\)
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