Transversal homoclinic points of a class of conservative diffeomorphisms

Abstract

We develop a global graph transformation to obtain estimates for certain invariant manifolds of a class of area preserving diffeomorphisms with symmetries. The existence of homoclinic or heteroclinic points and the analyticity of the angle between the invariant manifolds at them is proved for the Hénon and the standard maps. A lower bound of this angle is given for a large set of values of the parameters.