Once more on Hénon map: Analysis of bifurcations

Abstract

Using the analysis of bifurcations approach the detailed description of bifurcation phenomena in the classical Hénon map is presented. This description strongly supports the idea that the Hénon map contains all possible bifurcation phenomena known for two-dimensional discrete maps. It is interesting to note that the existence of two different equilibria in the Hénon map generates additional — dual — appearance of bifurcation phenomena. The proposed analysis can serve as a prototype of the bifurcation analysis for finite-dimensional iterative processes with multiple equilibria.