Description
![](../../doubling/s1.gif)
1D map
The period-doubling accumulation point in unimodal map of 6-th power.
For 1D maps with extremum and cubic inflection point - the limit of period-doubling
on a curve in the 3D parameter space defined by the condition "extremum
to iflection point" or vise versa.
More general systems
S-point appears generically in codimension 5, but the pseudo-S type may
occur, in codimension 3 as an intermediate asymptotics.
RG equation
![](../../doubling/s2.gif)
The fixed point
![](../../doubling/s3.gif)
The orbital scaling factor
![](../../doubling/s4.gif)
Critical multiplier
![](../../doubling/s5.gif)
Relevant eigenvalues
A
![](../../doubling/s6.gif)
B
![](../../doubling/s7.gif)
Codimension CoDim=5 (restr. 3)
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Codimension-3 example (SA type)
![](../../doubling/s8.gif)
![](../../doubling/s9.gif)
Parameter space scaling with factors
![](../../doubling/s14.gif)
Scaling coordinates
![](../../doubling/s10.gif)
![](../../doubling/s11.gif)
![](../../doubling/s12.gif)
![](../../doubling/s13.gif)
![](../../doubling/s15.gif)
show enlarged figure
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