Crossover from dissipative to conservative behaviour in period-doubling systems

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