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Critical Slowing Down in One-Dimensional Maps and Beyond

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Abstract

This is a brief review on critical slowing down near the Feigenbaum period-doubling bifurcation points and its consequences. The slowing down of numerical convergence leads to an “operational” fractal dimension D=2/3 at a finite order bifurcation point. There is a cross-over to D 0=0.538... when the order goes to infinity, i.e., to the Feigenbaum accumulation point. The problem of whether there exists a “super-scaling” for the dimension spectrum D W q that does not depend on the primitive word W underlying the period-n-tupling sequence seems to remain open

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Authors and Affiliations

  1. T-Life Research Center, Fudan University, Shanghai, 200433, China

    Bailin Hao

  2. Institute of Theoretical Physics, Academia Sinica, Beijing, 100080, China

    Bailin Hao

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  1. Bailin Hao
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Correspondence to Bailin Hao.

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Hao, B. Critical Slowing Down in One-Dimensional Maps and Beyond. J Stat Phys 121, 749–757 (2005). https://doi.org/10.1007/s10955-005-8669-3

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  • DOI: https://doi.org/10.1007/s10955-005-8669-3

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