Universal effects of dissipation in two-dimensional mappings

One can define an effective dissipation for highly iterated two-dimensional maps or recursion relations. The convergence rate δeff of the sequence of period-doubling bifurcations is shown to depend in a universal way on this effective dissipation in the limit of long 2ⁿ cycles. These conclusions are based on both a renormalization argument and numerical calculations. The paper concludes with a brief discussion of the implications for physical systems.