Journal article
Ergodic scales in fractal measures
Mathematics of Computation, Vol.81(278), pp.941-955
2012
DOI: 10.1090/S0025-5718-2011-02517-2
Abstract
We will consider a family of fractal measures on the real line which are fixed, in the sense of Hutchinson, under a finite family of contractive affine mappings. The maps are chosen such as to leave gaps on . Hence they have fractal dimension strictly less than . The middle-third Cantor construction is one example. Depending on the gaps and the scaling factor, it is known that the corresponding Hilbert space exhibits strikingly different properties. In this paper we show that when is fixed in a certain class, there are positive integers such that multiplication by modulo induces an ergodic automorphism on the measure space (support(), ).
Details
- Title: Subtitle
- Ergodic scales in fractal measures
- Creators
- Palle E.T Jorgensen
- Resource Type
- Journal article
- Publication Details
- Mathematics of Computation, Vol.81(278), pp.941-955
- DOI
- 10.1090/S0025-5718-2011-02517-2
- ISSN
- 0025-5718
- eISSN
- 1088-6842
- Language
- English
- Date published
- 2012
- Academic Unit
- Mathematics
- Record Identifier
- 9983985879402771
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