A QUANTITATIVE BIFURCATION-ANALYSIS OF HENON-LIKE 2D MAPS

We numerically study the bifurcations of two nonlinear maps, with the same linear part, which depend on a parameter namely the Henon quadrat ic map and the so called 'beam-beam' map. Many families of periodic or bits which bifurcate from the central family, are studied. Each family undergoes a sequence of period doubling bifurcations in the quadratic map. But the behavior of the 'beam-beam' map is completely different. Inverse bifurcations occur in both maps. But some families of the sam e type which bifurcate inversely in the quadratic map do not bifurcate inversely in the 'beam-beam' map, even though both maps have common l inear part.