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K. Dajani and C. Kalle
Local dimensions for the random β-transformation view print
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| Published: |
June 7, 2013 |
| Keywords: |
β-expansion, random transformation, Bernoulli convolution, local dimension, Pisot number |
| Subject: |
Primary, 37A05, 37C45, 11K16, 42A85. |
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Abstract
The random β-transformation K is isomorphic to a full shift. This relation gives an invariant measure for K that yields the Bernoulli convolution by projection. We study the local dimension of the invariant measure for K for special values of β and use the projection to obtain results on the local dimension of the Bernoulli convolution.
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| Acknowledgements
The second author was supported by NWO (Veni grant no. 639.031.140).
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| Author information
K. Dajani:
Department of Mathematics, Utrecht University, Postbus 80.000, 3508 TA Utrecht, the Netherlands
k.dajani1@uu.nl
C. Kalle:
Mathematical Institute, Leiden University, Postbus 9512, 2300 RA Leiden, the Netherlands
kallecccj@math.leidenuniv.nl
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