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Period-doubling critical behavior

E - Eight-power



1D maps
The period-doubling accumulation point in unimodal map of 8-th power. For 1D maps with three extrema - the limit of period-doubling on a curve in the 3D parameter space defined by the condition "extremum to extremum to extremum".

More general systems
E-point may appear generically in codimension 7. In some cases the pseudo-E type is expected to occur in codimension 3 (as an intermediate asymptotics).

RG equation

The fixed point

The orbital scaling factor

Critical multiplier

Relevant eigenvalues:

CoDim=7 (restr. 3)

Codimension-3 example


Parameter space scaling with factors

Scaling coordinates


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Saratov group
of theoretical nonlinear
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