  Time reversal of quantum dynamics can be achieved by a global change of the
Hamiltonian sign (a hasty Loschmidt daemon), as in the Loschmidt Echo
experiments in NMR, or by a local but persistent procedure (a stubborn daemon)
as in the Time Reversal Mirror (TRM) used in ultrasound acoustics. While the
first is limited by chaos and disorder, the last procedure seems to benefit
from it. As a first step to quantify such stability we develop a procedure, the
Perfect Inverse Filter (PIF), that accounts for memory effects, and we apply it
to a system of coupled oscillators. In order to ensure a many-body dynamics
numerically intrinsically reversible, we develop an algorithm, the pair
partitioning, based on the Trotter strategy used for quantum dynamics. We
analyze situations where the PIF gives substantial improvements over the TRM.
