Crossover from dissipative to conservative behaviour in period-doubling systems (Q1118226)

We investigate the crossover properties, between the conservative and dissipative limit, for period-doubling bifurcations in two-dimensional iterative maps; as a generic example we use the standard form of the Hénon map. The approximants to the Feigenbaum constant \(\delta\) lie on a universal crossover curve, which turns out to be non-monotonic. A similar curve is found for the scaling factor \(\alpha\). More generally, we discuss the crossover of the trajectory scaling function 1/\(\sigma\), and its properties in the conservative limit.