Period-doubling critical behavior

F - Feigenbaum alphabet
Description This type of critical behavior occurs during a one-parameter analysis of typical period-doubling transition to chaos in dissipative systems, in particular, in 1D maps. It is known after Feigenbaum, Cvitanovic, Coullet and Tresser.   RG equation   The fixed point of the RG equation   The orbital scaling factor   Critical multiplier   Relevant eigenvalue   Codimension CoDim=1	An example - logistic map The critical point at Parameter space arrangement show enlarged figure Scaling with factor show enlarged figure Scaling with factor show enlarged figure Other examples Ueda oscillator, Rossler oscillator, Lorenz system, Ikeda map, Henon map etc.

main science alphabet this page only top