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IRREGULAR SOLUTIONS OF THE FEIGENBAUM FUNCTIONAL EQUATION

We describe the structure of orbits generated by two commuting bijections and using this description we construct irregular solutions of the Feigenbaum functional equation: ip(<p( Ax)) = A <p(x) = 0 and its generalizations: yp(x) = s M / ( x ) ) ) . The graph of such a solution almost cover the plane in the sense of measure and topology.