Rauzy tilings and bounded remainder sets on the torus
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Publication:558746
DOI10.1007/s10958-006-0262-zzbMath1158.11331OpenAlexW2010933007MaRDI QIDQ558746
Publication date: 14 July 2005
Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/231301
Topological dynamics (37B99) Probabilistic theory: distribution modulo (1); metric theory of algorithms (11K99) Distribution modulo one (11J71)
Related Items (33)
Exchanged toric tilings, Rauzy substitution, and bounded remainder sets ⋮ Universal karyon tilings ⋮ Bounded remainder sets on a double covering of the Klein bottle ⋮ Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices ⋮ Local structure of karyon tilings ⋮ Symmetry properties of karyon tilings ⋮ Differentiation of induced toric tiling and multidimensional approximations of algebraic numbers ⋮ Bounded remainder sets ⋮ Periodic karyon expansions of cubic irrationals in continued fractions ⋮ Additive problem with \(k\) numbers of a special form ⋮ Rauzy fractals and their number-theoretic applications ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Embeddings of circular orbits and the distribution of fractional parts ⋮ Karyon expansions of Pisot numbers in multidimensional continued fractions ⋮ Induced bounded remainder sets ⋮ Convex polyhedra with deltoidal vertices ⋮ A local algorithm for constructing derived tilings of the two-dimensional torus ⋮ Bounded remainder polyhedra ⋮ Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices. II. ⋮ Parametrization of a two-dimensional quasiperiodic Rauzy tiling ⋮ The karyon algorithm for expansion in multidimensional continued fractions ⋮ Unimodularity of induced toric tilings ⋮ Unimodular invariance of karyon expansions of algebraic numbers in multidimensional continued fractions ⋮ Bounded remainder sets under torus exchange transformations ⋮ One-dimensional quasiperiodic tilings admitting progressions enclosure ⋮ Dividing toric tilings and bounded remainder sets ⋮ Fibonacci-even numbers: Binary additive problem, distribution over progressions, and spectrum ⋮ Bounded remainder sets for rotations on the adelic torus ⋮ Тригонометрические интегралы над одномерными квазирешетками произвольной коразмерности ⋮ Multidimensional Hecke theorem on the distribution of fractional parts ⋮ Moduli of toric tilings into bounded remainder sets and balanced words
Cites Work
- Unnamed Item
- On Rauzy fractal
- Arithmetic and dynamical properties of the Rauzy fractal
- Modified Jacobi-Perron algorithm and generating Markov partitions for special hyperbolic toral automorphisms
- On the boundary of self-affine tilings generated by Pisot numbers
- Nombres algébriques et substitutions
- One-dimensional Fibonacci tilings
- Bounded remainder sets
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