Homoclinic Orbits in the Complex Domain
V. F. Lazutkin, Carles Simó · International Journal of Bifurcation and Chaos · 1997
We consider the standard map, as a paradigm of area preserving map, when the variables are taken as complex. We study how to detect the complex homoclinic points, which cannot dissappear under a homoclinic tangency. This seems a promising tool to understand the stochastic zones of area preserving maps. The paper is mainly phenomenological and includes theoretical support to the observed phenomena. Several conjectures are stated.