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Journal of Statistical Physics

, Volume 121, Issue 5–6, pp 749–757 | Cite as

Critical Slowing Down in One-Dimensional Maps and Beyond

  • Bailin Hao
Article

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 D0=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

Keywords

Period doubling attractor fractal dimension critical slowing down 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.T-Life Research CenterFudan UniversityShanghaiChina
  2. 2.Institute of Theoretical PhysicsAcademia SinicaBeijingChina

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