Period-doubling in discrete relative spatial dynamics and the Feigenbaum sequence

It is shown in this paper that although the period-doubling Feigenbaum sequence and the associated universal numbers in discrete maps of the logistic type hold over parameters, their true nature have them holding over slopes of the corresponding Poincaré maps. This finding enables one to find these Feigenbaum slope sequences in more complex maps. Further, it is demonstrated by an example in discrete relative growth spatial dynamics that a Feigenbaum sequence does not hold over the bifurcation parameter.