Homoclinic orbits in the complex domain

V. F.Lazutkin, Physics Department, St.-Petersburg State University,
   Ulyanov str. 1, kor.1, Petrodvorets, St.-Petersburg, 198904, Russia

C. Sim\'o, Departament de Matem\`atica Aplicada i An\`alisi,
   Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

Abstract

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 can not 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.