A Computer-Assisted Proof of Universality for Area-Preserving Maps

I. Analysis of doubling: Feigenbaum universality for area-preserving maps Generating functions Further reduction of the problem Spectral properties Constructions of the operator $L$ Construction of the doubling operator; II. Functional analysis on the computer: Interval and neighborhood arithmetics Spectral theory Interval and neighborhood arithmetics on a computer List of correspondences; III. Proofs: Computer program Program output Table 1.