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Feigenbaum showed that for discrete 1D systems with a (smooth) unimodal evolution function, the route to chaos is universal, and depends only on the order of the map's maximum.

Are there analogous results for multidimensional maps? (In particular, I'm interested in 2D)

How about systems with multiple order parameters? In such cases in general the onset of chaos is not a point, but a surface. So the bifurcation patterns are probably dependent on the path chosen in parameter space. Are there still universal aspects that hold for different systems?

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