World Scientific
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

GENERAL FORM OF SUPERUNIVERSALITY FOR FRACTAL DIMENSIONS IN ONE-DIMENSIONAL MAPS

    https://doi.org/10.1142/S0217979201007956Cited by:2 (Source: Crossref)

    In one-dimensional continuous maps, there is an internal relationship between equivalent scaling factors αe and fractal dimensions d of Feigenbaum-type attractors on all critical (accumulation) points of transitions to chaos. In general, for m-modal maps with m turning points C1,C2,…,Cm, by defining αe as the geometric average of all scaling factors αCi(i=1,2,…,m), |αe| =|αC1 αC2… αCm|1/m, the superuniversal relationship d(W)log|W|e(W)|=β(e) holds, where |W| is the basic period of the m-tuply superstable sequences W, and β(e) is not only independent of the concrete sequences W, but also independent of the concrete maps. This is a general superuniversality for arbitrary multimodal maps, which is verified numerically for the cases of m ≤ 3 and can also be extended to Lorenz maps with a discontinuous point.

    PACS: 05.45.-a, 45.05.+x, 03.20.+i
    You currently do not have access to the full text article.

    Recommend the journal to your library today!