Heteroclinic orbits and transport in a perturbed integrable standard map
  Explicit formulae are given for the saddle connection for an integrable family of standard maps studied by Suris. A generalization of Melnikov's method shows that, upon perturbation, this connection is destroyed. We give explicit formula for the first order approximation of the area of the lobes of the resultant turnstile. It is shown that the lobe area is exponentially small in the limit when the Suris map approaches the trivial twist map. 
Hector E. Lomeli and James D. Meiss