Bifurcation analysis of the Henon map

Division of the parameter plane for the two-dimensional Henon mapping into domains of periodic and chaotic oscillations is studied numerically and ana lytically. Regularities in the occurrence of different motions and transiti ons are analyzed. It is shown that there are domains in the plane of parame ters, where non-uniqueness of motions exists. This may lead to abrupt chang es of the character of the dynamics under variation in the parameters, that is, to a sudden transition from one stable cycle to another or to chaotiza tion of the oscillations.