Gupte, Neelima ; Amritkar, R. E. (1989) New dimension in multifractals: the exponential dimension Physical Review A, 39 (10). pp. 5466-5469. ISSN 1050-2947
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Official URL: http://pra.aps.org/abstract/PRA/v39/i10/p5466_1
Related URL: http://dx.doi.org/10.1103/PhysRevA.39.5466
Abstract
We propose a new dimension, the exponential dimension, to take proper account of the harmonic lengths that vary inversely to the stage of refinement in the multifractal measure. The need for this dimension arises due to the infinite singularity index which is otherwise obtained with these lengths. We find such a dimension in the Julia set and the circle map. We obtain a phase transition in these sets signaled by a crossover from exponential to generalized dimension. This is due to a switch from the dominance of the harmonic lengths to that of the geometric lengths.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to American Physical Society. |
| ID Code: | 476 |
| Deposited On: | 21 Sep 2010 10:35 |
| Last Modified: | 12 May 2011 05:17 |
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