Collision of Feigenbaum cascades

G.L. Oppo, A. Politi

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


The existence in dynamical systems of chaotic bands delimited on both sides by period-doubling cascades is a general two-parameter phenomenon. Here we show evidence that, whenever these chaotic regions disappear, the bifurcation convergence rate undergoes a slowing down and asymptotically approaches the square root of the universal number =4.6692. A simple renormalization-group analysis is performed to explain this critical behavior and its scaling properties. In particular a theoretical universal function describing the evolution of the convergence rate from 12, to is given and numerically verified.
Original languageEnglish
Pages (from-to)435-441
Number of pages7
JournalPhysical Review A
Issue number1
Publication statusPublished - 1 Jul 1984


  • chaotic bands
  • bifurcation convergence rate
  • renormalization-group analysis
  • dynamical systems


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