Critical Slowing Down in One-Dimensional Maps and Beyond

Bailin Hao
2005 Journal of statistical physics  
This is a brief review on critical slowing down near the Feigenbaum perioddoubling 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
more » ... word W underlying the period-n-tupling sequence seems to remain open.
doi:10.1007/s10955-005-8669-3 fatcat:52vy724gp5f55j3lviqthodykq