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Medientyp:
E-Artikel
Titel:
ERGODIC SCALES IN FRACTAL MEASURES
Beteiligte:
JORGENSEN, PALLE E. T.
Erschienen:
American Mathematical Society, 2012
Erschienen in:Mathematics of Computation
Sprache:
Englisch
DOI:
10.1090/S0025-5718-2011-02517-2
ISSN:
0025-5718;
1088-6842
Entstehung:
Anmerkungen:
Beschreibung:
<p>We will consider a family of fractal measures on the real line ℝ 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 ℝ. Hence they have fractal dimension strictly less than 1. The middle-third Cantor construction is one example. Depending on the gaps and the scaling factor, it is known that the corresponding Hilbert space L 2 (μ) exhibits strikingly different properties. In this paper we show that when μ is fixed in a certain class, there are positive integers p such that multiplication by p modulo 1 induces an ergodic automorphism on the measure space (support(μ), μ).</p>