Exponentially Small Splitting of Separatrices for Perturbed Integrable Standard-Like Maps

Summary. The splitting of separatrices for the standard-like maps is measured. For even entire perturbative potentials such that , where is the Borel transform of V(y) , the following asymptotic formula for the area A of the lobes between the perturbed separatrices is established: This formula agrees with the one provided by the Melnikov theory, which cannot be applied directly, due to the exponentially small size of A with respect to h . Received April 8, 1997; revised August 25, 1997, and accepted August 27, 1997