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Period-doubling critical behavior

S - Six-power



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

The fixed point

The orbital scaling factor

Critical multiplier

Relevant eigenvalues


CoDim=5 (restr. 3)

Codimension-3 example (SA type)


Parameter space scaling with factors

Scaling coordinates


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Saratov group
of theoretical nonlinear
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