V. Gelfreich
A proof of the exponentially small transversality
of the separatrices for the Standard Map
(222K, LaTeX 2.09)
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.