Statistical properties of some spatially discretized dynamical systems

Computer simulations of dynamical systems are spatial discretizations in wh ich the finite machine arithmetic space replaces the continuum state space of the original system. Any trajectory of a spatial discretization of a dyn amical system is thus eventually periodic, so the dynamical behaviour of su ch computations are essentially determined by the cycles of the discretized map. Such dynamical behaviour depends seemingly randomly on the fineness o f the discretization mesh. In this paper statistical properties of the maxi mal cycles of spatial discretizations are investigated for some systems suc h as the tent map, rotations on a circle and toral endomorphisms.