  In this paper, we are concerned with the construction and analysis of a new
class of methods obtained as double jump compositions with complex coefficients
and projection on the real axis. It is shown in particular that the new
integrators are symmetric and symplectic up to high orders if one uses a
symmetric and symplectic basic method. In terms of efficiency, the
aforementioned technique requires fewer stages than standard compositions of
the same orders and is thus expected to lead to faster methods.
