Any horizontal component to the motion can be ignored. The only thing of interest is the vertical motion of the ball in a gravitational field.
There is an elastic collision between the ball and the flat surface. Unlike an inelastic collision, energy is not conserved. Energy is lost when the ball hits the surface and rebounds; it shows up as heat in the ball and at the surface at the point of collision. Assuming the surface is very hard, most of the heat goes into the ball.
At some point the kinetic energy remaining is not enough to lift the ball against gravity so the ball does not get lifted off the surface. If you follow the center of mass of the ball, it continues to oscillate, compressing and expanding elastically until the remaining kinetic energy is expended as heat. As the size of the oscillations get smaller and smaller you eventually reach a scale where the idealized model of the ball begins to fail; at that point, things become complicated.
There is an elastic collision between the ball and the flat surface. Unlike an inelastic collision, energy is not conserved. Energy is lost when the ball hits the surface and rebounds; it shows up as heat in the ball and at the surface at the point of collision. Assuming the surface is very hard, most of the heat goes into the ball.
At some point the kinetic energy remaining is not enough to lift the ball against gravity so the ball does not get lifted off the surface. If you follow the center of mass of the ball, it continues to oscillate, compressing and expanding elastically until the remaining kinetic energy is expended as heat. As the size of the oscillations get smaller and smaller you eventually reach a scale where the idealized model of the ball begins to fail; at that point, things become complicated.