CONTENTS Introduction.............................................................................................. 3 I. The role of the computing machine................................................. 12 II. Limit sets.............................................................................................. 21 III. The "Δt-modification"......................................................................... 30 IV. Modification of the coefficients........................................................ 36 V. Relation to the theory of differential equations............................. 45 VI. Broken-linear transformations in two dimensions..................... 47 Appendix I................................................................................................. 51 Appendix II................................................................................................ 61