Geodesic
Splitting of separatrices: perturbation theory and exponential smallness
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 56 (2001) no. 3, pp. 499-558

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This is a survey of the main results related to separatrix splitting for area-preserving maps and Hamiltonian systems with one and a half degrees of freedom. Special attention is paid to problems in which the separatrix splitting is exponentially small with respect to the perturbation parameter. 
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     author = {V. G. Gelfreich and V. F. Lazutkin},
     title = {Splitting of separatrices: perturbation theory and exponential smallness},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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V. G. Gelfreich; V. F. Lazutkin. Splitting of separatrices: perturbation theory and exponential smallness. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 56 (2001) no. 3, pp. 499-558. http://geodesic.mathdoc.fr/item/RM_2001_56_3_a1/