ABSTRACT

Infinite sequences of period doubling bifurcations in one-parameter families (1-pf) of maps enjoy very strong universality properties: This is known numerically in a multitude of cases and has been shown rigorously for certain 1-pf of maps on the interval. These bifurcations occur in 1-pf of analytic maps at values of the parameter tending to a limit with the asymptotically geometric ratio 1/4.6692 … .In this paper we indicate the main steps of a proof that the same is true for 1-pf of analytic maps from ℂ n to ℂ n, whose restriction to ℝ n is real.