Analytical Conditions for the Appearance of Homoclinic and Heteroclinic Points of a 2-dimensional Mapping ---The Case of the Hénon Mapping---
A method is proposed to obtain analytical conditions for the appearance of homoclinic and heteroclinic points of a class of 2-dimensional mappings with a small parameter. It consists of solving a functional equation, which is satisfied by invariant curves, perturbatively and combining the results with simple geometrical consideration. The mapping proposed by Hénon is treated here, for which it is also found that the appearance of heteroclinic points results in the disappearance of a strange attractor. The results are in good agreement with those of numerical simulations.