  A competition between decay and growth of energy in a time-dependent stadium
billiard is discussed giving emphasis in the decay of energy mechanism. A
critical resonance velocity is identified for causing of separation between
ensembles of high and low energy and a statistical investigation is made using
ensembles of initial conditions both above and below the resonance velocity.
For high initial velocity, Fermi acceleration is inherent in the system.
However for low initial velocity, the resonance allies with stickiness hold the
particles in a regular or quasi-regular regime near the fixed points,
preventing them from exhibiting Fermi acceleration. Also, a transport analysis
along the velocity axis is discussed to quantify the competition of growth and
decay of energy and making use distributions of histograms of frequency, and we
set that the causes of the decay of energy are due to the capture of the orbits
by the resonant fixed points.
