-expansions with deleted digits

for Pisot numbers

Author:
Steven P. Lalley

Journal:
Trans. Amer. Math. Soc. **349** (1997), 4355-4365

MSC (1991):
Primary 11K55, 28A78

DOI:
https://doi.org/10.1090/S0002-9947-97-02069-2

MathSciNet review:
1451608

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Abstract | References | Similar Articles | Additional Information

Abstract: An algorithm is given for computing the Hausdorff dimension of the set(s) of real numbers with representations , where each , a finite set of ``digits'', and is a Pisot number. The Hausdorff dimension is shown to be , where is the top eigenvalue of a finite 0-1 matrix , and a simple algorithm for generating from the data is given.

**1.**Bowen, R. (1975) Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms.*Springer Lecture Notes in Math.***470**. MR**56:1364****2.**Falconer, K. (1985)*The Geometry of Fractal Sets*. Cambridge Univ. Press. MR**88d:28001****3.**Keane, M., Smorodinsky, M., and Solomyak, B. (1995) On the morphology of expansions with deleted digits.*Trans. Amer. Math. Soc.***347**, 955-966. MR**95h:11079****4.**Parry, W. (1964) Intrinsic Markov chains.*Trans. Amer. Math. Soc.***112**, 55-64. MR**28:4579****5.**Pollicott, M. and Simon, K. (1995) The Hausdorff dimension of expansions with deleted digits.*Trans. Amer. Math. Soc.***347**, 967-983. MR**95h:11080**

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Additional Information

**Steven P. Lalley**

Affiliation:
Department of Statistics, Mathematical Sciences Bldg., Purdue University, West Lafayette, Indiana 47907

Email:
lalley@stat.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9947-97-02069-2

Keywords:
Hausdorff dimension,
entropy,
Pisot number

Received by editor(s):
June 12, 1995

Additional Notes:
Supported by NSF grant DMS-9307855

Article copyright:
© Copyright 1997
American Mathematical Society