Description
![](../../doubling/f1.gif)
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
![](../../doubling/f14.gif)
The fixed point of the RG equation
![](../../doubling/f5.gif)
The orbital scaling factor
![](../../doubling/f6.gif)
Critical multiplier
![](../../doubling/f7.gif)
Relevant eigenvalue
![](../../doubling/f8.gif)
Codimension
CoDim=1
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An example - logistic map
![](../../doubling/f10.gif)
The critical point at
![](../../doubling/f11.gif)
Parameter space arrangement
![](../../doubling/f2.gif)
show enlarged figure
Scaling with factor
![](../../doubling/f12.gif)
![](../../doubling/f3.gif)
show enlarged figure
Scaling with factor
![](../../doubling/f13.gif)
![](../../doubling/f4.gif)
show enlarged figure
Other examples
Ueda oscillator, Rossler oscillator, Lorenz system, Ikeda map, Henon map
etc.
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