A New Multidimensional Slow Continued Fraction Algorithm and Stepped Surface

DOI10.1080/10586458.2014.917597zbMath1335.11055arXiv1310.7781OpenAlexW1987582727MaRDI QIDQ5498925

Shunji Ito, Jun-ichi Tamura, Asaki Saito, Shin-ichi Yasutomi, Maki Furukado

Publication date: 11 February 2015

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.7781

zbMATH Keywords

tilingcontinued fractionPisot numberSturmian sequenceFarey mapstepped surfacereal cubic number fieldmulti-dimensional continued fraction algorithm

Mathematics Subject Classification ID

Combinatorics on words (68R15) Continued fractions and generalizations (11J70) Symbolic dynamics (37B10) Continued fraction calculations (number-theoretic aspects) (11Y65) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (8)

Pseudorandom number generator based on the Bernoulli map on cubic algebraic integers ⋮ Differentiation of induced toric tiling and multidimensional approximations of algebraic numbers ⋮ Periodic karyon expansions of cubic irrationals in continued fractions ⋮ Periodic karyon expansions of algebraic units in multidimensional continued fractions ⋮ Simplex-module algorithm for expansion of algebraic numbers in multidimensional continued fractions ⋮ Karyon expansions of Pisot numbers in multidimensional continued fractions ⋮ Unimodularity of induced toric tilings ⋮ Unimodular invariance of karyon expansions of algebraic numbers in multidimensional continued fractions

Cites Work

• Brun expansions of stepped surfaces
• Modified Jacobi-Perron algorithm and generating Markov partitions for special hyperbolic toral automorphisms
• Parallelogram tilings and Jacobi-Perron algorithm
• Discrete planes, \({\mathbb Z}^2\)-actions, Jacobi-Perron algorithm and substitutions
• On simultaneous approximation to \((\alpha,\alpha^2)\) with \(\alpha^3+k\alpha-1=0\).
• A new multidimensional continued fraction algorithm
• Algebraic Jacobi-Perron algorithm for biquadratic numbers
• An Elementary Proof of Abramov’s Result on the Entropy of a Flow

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