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### Open Access Journals

DCDS

The techniques, based on formal series and combinatorics, used
nowadays to analyze numerical integrators may be applied to
perform high-order averaging in oscillatory periodic or
quasi-periodic dynamical systems. When this approach is employed,
the averaged system may be written in terms of (i) scalar
coefficients that are universal, i.e. independent of the system
under consideration and (ii) basis functions that may be written
in an explicit, systematic way in terms of the derivatives of the
Fourier coefficients of the vector field being averaged. The
coefficients may be recursively computed in a simple fashion. We
show that this approach may be used to obtain exponentially small
error estimates, as those first derived by Neishtadt. All the
constants that feature in the estimates have a simple explicit
expression.

## Year of publication

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