Cascade of Attractor-Merging Crises to the Critical Golden Torus and Universal Expansion-Rate Spectra

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Abstract
Two chaotic attractors with rotation number ρm=Fm-1/Fm, Fm being the m-th Fibonacci number, and ρm+1 just before their attractor-merging crisis converge to the critical golden torus as m→∞. A critical scaling is shown to hold for those chaotic attractors for large m, leading to a universal spectrum of the local expansion rates of nearby orbits.

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