BOUNDEDNESS AND DISSIPATIVITY OF TRUNCATED ROTATIONS ON UNIFORM PLANAR LATTICES

The finiteness of computer arithmetic can lead to some dramatic differ ences between the behaviour of a continuous dynamical sa stem and a co mputer simulation. A thorough rigorous theoretical analysis of what ma y or what does happen is usually extremely difficult and to date littl e has been done even in relatively simple contests. The comparative be haviour of a rotation mapping in the plane and on a uniform lattice in the plane is one such example. Simulations show that the rounding ope rator applied to a planar rotation mapping more or less preserves the qualitative behaviour of the original mapping, whereas the application of the truncation operator to a planar rotation can lead to quite dif ferent dynamical features. In this paper a theoretical justification o f the properties of the planar rotation mappings under truncation to a uniform integer lattice is provided, in particular properties of boun dedness and dissipativity are investigated.