On dynamics of the Henon map

Abstract

Division of the parameter plane for the two—dimensional Henon mapping into domains of periodic and chaotic oscillations is studied numerically and analytically. Regularities in the occurrence of different motions and bifurcational transitions are analyzed. It is shown that there are domains in the plane of parameters, where non—uniqueness of motions exists. This may lead to abrupt changes of the character of the dynamics under variation in the parameters, that is, to а sudden transition from one stable cycle to another or to chaotization of the oscillations.