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

TF - Torus Fractalization alphabet

Description This type of critical behavior occurs in two-parameter analysis of 1D maps locally approximated by fractional-linear map and forced with the golden-mean frequency. The critical point separates the situations of smooth and fractal tori-collision on the bifurcation curve. RG equation The fixed point of the RG equation in class of fractional-linear maps , a(u)=3.1801-3.4507u-3.2471u2+Е b(u)=0.3299-0.0030u-8.3305u2+Е c(u)=-1-0.6015u+0.4438u2+Е d(u)=0.2107+0.1672u+3.0628u2+Е The orbital scaling factors Relevant eigenvalues Codimension CoDim=2 (For 1D map, and, presumably, for more general systems too)

An example: the forced map The critical point is located at Parameter space arrangement Scaling coordinates show enlarged figure Critical attractor: scaling with Scaling coordinates show enlarged figure

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