Spectral properties of the period-doubling operator

We compute the spectrum of the Feigenbaum period-doubling operator in the space of bounded analytical functions in an ellipse. The spectral properties of the period-doubling operator in this space are not the same as in the space of even analytical functions. In particular, it was found that the dimension of the unstable manifold is not one (Feigenbaum's conjecture), but three. We analyze several articles devoted to this problem and compare different approaches and algorithms.