98-270 V. Gelfreich

A proof of the exponentially small transversality of the separatrices for the Standard Map (222K, LaTeX 2.09) Apr 13, 98

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Abstract. In 1984 V. F. Lazutkin obtained an asymptotic formula for the separatrix splitting angle for the standard map. The proof was based on two conjectures. Probably, the original form of those conjectures was wrong, but Lazutkin's method was very efficient and inspired a large number of studies on the exponentially small splitting of separatrices. The consequent works prepared the base for a complete proof. The present paper contains a complete and self-contained proof of a refined version of the original formula. In this form the formula appeared first in a paper by Lazutkin, Svanidze and the author (Physica D 71(2):82-101, 1994). The proof is inspired by the ideas of Lazutkin original paper.

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