The \(\beta\)-transformation with a hole

DOI10.3934/DCDS.2016.36.1249zbMath1369.37017arXiv1412.6384OpenAlexW3098203872MaRDI QIDQ256134

Lyndsey Clark

Publication date: 9 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.6384

zbMATH Keywords

symbolic dynamicscombinatorics on wordsbeta expansionextremal pairsopen dynamical system

Mathematics Subject Classification ID

Combinatorics on words (68R15) Permutations, words, matrices (05A05) Measure-preserving transformations (28D05) Symbolic dynamics (37B10)

Related Items (8)

The baker’s map with a convex hole ⋮ Two bifurcation sets arising from the beta transformation with a hole at 0 ⋮ Critical values for the -transformation with a hole at ⋮ Subshifts of finite type and self-similar sets ⋮ The -transformation with a hole at 0 ⋮ Open maps: small and large holes with unusual properties ⋮ The \(k\)-transformation on an interval with a hole ⋮ The bifurcation set as a topological invariant for one-dimensional dynamics

Cites Work

• Unnamed Item
• Supercritical holes for the doubling map
• On cycles for the doubling map which are disjoint from an interval
• Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps
• Balanced words
• Digit frequencies of beta-expansions
• The classification of topologically expansive lorenz maps
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• Ordered orbits of the shift, square roots, and the devil's staircase
• Rotation orbits and the Farey tree
• The doubling map with asymmetrical holes

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