Maass forms are at 1 bifurcation. I don't know what's at two bifurcations. I think the hyperbolic Laplacian of whatever's at two bifurcations might equal the Maass forms at 1. The nodal set remains fixed but there's an amplitude everywhere else: that's one-periodic.
(speculative) continuous spectrum + discrete spectrum + and now let me go out on a limb: there's an analogue of a power series here, and there are more terms.. but they're all precisely 0 when there's no change of state.
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If you've ever played around with fractals/functions with the conjugate operation, you know of phenomena where a curve splitting the plane into two regions can just kind of /condense/. Again, this is completely speculative.
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