New dimension in multifractals: the exponential dimension

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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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.

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Deposited On:21 Sep 2010 10:35
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