The universal behavior of certain iterated nonlinear function maps (ie period doubling bifurcation route to chaos): xi+1=f(xi)
The usual method of solving the Hartree-Fock equations for interacting fermions is a nonlinear iterated functional mapping: fi+1(x)=F[fi+1(x),Vi[fi(x)]]
Since this mapping is nonlinear it is conceivable that convergence of the iteration may not occur and that something related to the period doubling bifurcations of nonlinear iterated function maps may result. In fact, I found such a situation during research I conducted in 1975.
My question is: has anyone else encountered such situations either in Hartree-Fock calculations or any other physics calculations that employ nonlinear iterated functional mappings?
A secondary question is: are there published mathematical investigations of nonlinear behavior in iterated functional maps?
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