A new type of period-doubling scaling behavior in two-dimensional area-preserving map

A novel type of period-doubling scaling behavior in two-dimensional area-preserving maps is reported, a conservative analog of the critical behavior in period-doubling one-dimensional maps with quartic extremum. We present data of numerical solution of the two-dimensional version of the Feigenbaum-Cvitanović RG equation and accurate estimates for the universal constants. Illustrations are given for self-similarity in the phase space and in the parameter space of the model map.