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Beta-Expansions with Negative Bases
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Shunji Ito
Published/Copyright:
August 20, 2009
Abstract
This paper investigates representations of real numbers with an arbitrary negative base –β < –1, which we call the (–β)-expansions. They arise from the orbits of the (–β)-transformation which is a natural modification of the β-transformation. We show some fundamental properties of (–β)-expansions, each of which corresponds to a well-known fact of ordinary β-expansions. In particular, we characterize the admissible sequences of (–β)-expansions, give a necessary and sufficient condition for the (–β)-shift to be sofic, and explicitly determine the invariant measure of the (–β)-transformations.
Received: 2008-10-10
Accepted: 2009-02-17
Published Online: 2009-08-20
Published in Print: 2009-August
© de Gruyter 2009
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- Symmetric CNS Trinomials
- On the β-Expansion of an Algebraic Number in an Algebraic Base β
- A Planar Integral Self-Affine Tile with Cantor Set Intersections with Its Neighbors
- Beta-Expansions with Negative Bases
- Convergence in Möbius Number Systems
- Factor Complexity of Infinite Words Associated with Non-Simple Parry Numbers
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Articles in the same Issue
- Preface
- Symmetric CNS Trinomials
- On the β-Expansion of an Algebraic Number in an Algebraic Base β
- A Planar Integral Self-Affine Tile with Cantor Set Intersections with Its Neighbors
- Beta-Expansions with Negative Bases
- Convergence in Möbius Number Systems
- Factor Complexity of Infinite Words Associated with Non-Simple Parry Numbers
- On the Boundary of the Set of the Closure of Contractive Polynomials
- Christoffel Words and Markoff Triples
- Characterizations of Words with Many Periods
