Multifractals in polynomial circle maps

The singularity spectrum ⨍(α) and the generalised dimensions D q of the chaotic attractor associated with the quasiperiodic route in polynomial circle maps are analysed using the perturbative scheme. It is found that D q in general depends on the order of the inflection point, z, of the map, but D 0...

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Bibliographic Details
Published in:Physics letters. A 1992-05, Vol.165 (3), p.231-234
Main Authors: Valsamma, K.M., Ambika, G., Joseph, K.Babu
Format: Article
Language:English
Subjects:
Exact sciences and technology
Nonlinear dynamics and nonlinear dynamical systems
Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
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Summary:The singularity spectrum ⨍(α) and the generalised dimensions D q of the chaotic attractor associated with the quasiperiodic route in polynomial circle maps are analysed using the perturbative scheme. It is found that D q in general depends on the order of the inflection point, z, of the map, but D 0 seems to be independent of z and is equal to 1. The ⨍-α curves for large z tend to be relatively flat near the maximum. We also establish a universal relation connecting the minimum and maximum values of α.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(92)90041-J