DETERMINATION OF THE STABLE PERIODIC ORBITS FOR THE HÉNON MAP BY ANALYTICAL METHOD

This paper is concerned with the general conditions of the existence of a stable period-N orbit for the Hénon map. The critical parameter values of Its "window" and destabilizing location are determined exactly by an analytical method. Our theoretical results agree with Hamouly and Mira's numerical calculations very well. We find that the mutual relations between the two window curves of the period-5 orbit and their corresponding destabilizing curves are changed.