Multifractal description of singular measures in dynamical systems
- 1 October 1987
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 36 (8) , 4104-4106
- https://doi.org/10.1103/physreva.36.4104
Abstract
We analyze the recent work by Halsey et al. [Phys. Rev. A 33, 1141 (1986)] on the characterization of certain singular measures in dynamical systems in terms of algebraic singularities of strength α and their dimensions f(α). Analytic study of the two-scale Cantor set suggests that these singularities are only virtual in nature and f(α), which has previously been interpreted as the fractal dimension for the subset of singularities of strength α, is not so. Modified interpretation of f(α) is provided.Keywords
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