Evidence for a new period-doubling sequence in four-dimensional symplectic maps

Abstract

We have numerically investigated period-doubling bifurcations in four-dimensional symplectic maps. Our study indicates the existence of a universally self-similar period-doubling sequence. Unlike the two-dimensional case, the fixed-point map has two unstable directions under the period-doubling operator with two relevant eigenvalues 8.721 097 2 and -15.0786. The four orbital scaling factors along and across the dominant symmetry surface are, respectively, 16.1449, -4.018 07, 16.36, and -7.5393.