Statistical properties of discretizations of a class of chaotic dynamical systems

Computer simulations of dynamical systems contain discretizations, where finite machine arithmetic replaces continuum state spaces. In some circumstances, complicated theoretical behavior has a tendency to collapse to trivial and degenerate behavior as a result of discretizations. Various statistical estimators associated with such collapsing effects often seem to depend on the corresponding discretization in a random way. Behavior of some statistical properties of collapse is discussed. Results of computer modeling of mappings x 1 − ¦1 − 2x¦l, x ε [0, 1], l > 2 are presented.