  A system plus environment conservative model is used to characterize the
nonlinear dynamics when the time averaged energy for the system particle starts
to decay. The system particle dynamics is regular for low values of the $N$
environment oscillators and becomes chaotic in the interval $13\le N\le15$,
where the system time averaged energy starts to decay. To characterize the
nonlinear motion we estimate the Lyapunov exponent (LE), determine the power
spectrum and the Kaplan-Yorke dimension. For much larger values of $N$ the
energy of the system particle is completely transferred to the environment and
the corresponding LEs decrease. Numerical evidences show the connection between
the variations of the {\it amplitude} of the particles energy time oscillation
with the time averaged energy decay and trapped trajectories.
