On the symbolic dynamics of the Henon map

Abstract

The authors study a method for finding all periodic orbits of the dissipative Henon map. For the 'canonical' values a=1.4, b=0.3 this method is found to give indeed the good symbolic dynamics proposed earlier by two of them, but it does not work as proposed for larger values of b. This is seen in two ways. Although the method is thus not universally valid, it can be used to study problems related to periodic orbits. They find that (for the usual values a=1.4, b=0.3) expressions for average quantities are not easily obtained precisely from periodic orbits, in agreement with recent claims.