Geometrical approach to the splitting of separatrix for standard-like mappings

In standard-like mappings. a series of homoclinic points of the stable and unstable manifolds of the fixed saddle appear on the symmetry axis of the r eversibility through tangent bifurcation with the increase of parameter a. We introduce critical parameter values a(n). n = 1.2..... for this bifurcat ion. A simple geometrical consideration of mapping of an area in the limit a --> 0 gives us the relation of the splitting angle of the stable and unst able manifolds and the functional dependence of a(n) on n. A mapping which shows a non-exponential splitting is considered for comparison. (C) 2001 El sevier Science B.V. All rights reserved.