  We consider background dynamics of generalized Galileon theories in the
context of inflation, where gravity and inflaton are non-minimally coupled to
each other. In the inflaton oscillation regime, the Hubble parameter and energy
density oscillate violently in many cases, in contrast to the Einstein gravity
with minimally coupled inflaton. However, we find that there is an adiabatic
invariant in the inflaton oscillation regime in any generalized Galileon
theory. This adiabatic invariant is useful in estimating the expansion law of
the universe and also the particle production rate due to the oscillation of
the Hubble parameter.
