An averaging method for Hamiltonian systems, exponentially close to integrable ones.

Exponentially small separatrix splitting for a pendulum with rapidly oscillating suspension point and for the standard Chirikov map is studied by means of a new averaging method, which is a continuous version of the Neishtadt averaging procedure. An asymptotic formula for the rate of the separatrix splitting is obtained. (c) 1996 American Institute of Physics.

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