Period-doubling critical behavior

E - Eight-power alphabet

Description 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: Codimension CoDim=7 (restr. 3)

Codimension-3 example   Parameter space scaling with factors Scaling coordinates   show enlarged figure

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