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Critical behavior associated with quasiperiodicity at the golden-mean frequency ratio

GM - Golden Mean classic

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Description

This type of critical behavior occurs in two-parameter analysis of transition to chaos via the two-dimensional torus. It is known after Feigenbaum, Kadanoff, Shenker; Rand, Ostlund and Siggia.

 

RG equation

 

The fixed point of the RG equation
g(x)=1+0.7652x3-0.2155x6-0.0535x9+...

 

The orbital scaling factor

 

Critical multiplier
(for periodic orbits of Fibonacci periods in complex domain)

 

Relevant eigenvalues

 

Codimension
CoDim=2

Circle map


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Attractor scaling with


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Parameter space


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Scaling with

Scaling coordinates


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Saratov group
of theoretical nonlinear
dynamics
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