Critical Slowing Down in One-Dimensional Maps and Beyond

Author: Hao Bailin  

Publisher: Springer Publishing Company

ISSN: 0022-4715

Source: Journal of Statistical Physics, Vol.121, Iss.5-6, 2005-12, pp. : 749-757

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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 q W that does not depend on the primitive word W underlying the period-n-tupling sequence seems to remain open