Why computers like Lebesgue measure (Q1118058)

This paper deals with computer chaos versus true trajectory chaos. It has been observed in practice that the histograms of computer simulations seem to display the invariant measure that is absolutely continuous with respect to the Lebesgue measure; and an explanation of this phenomenon is herein proposed. After emphasis on the deficiencies of the random perturbation models, the relation between computer orbits and absolutely continuous invariant measures is exhibited, and then it is shown that a large class of piecewise linear transformations have long periodic trajectory.