Quantized linear systems on integer lattices: a frequency-based approach

The roundoff errors in computer simulations of continuous dynamical systems, caused by finiteness of machine arithmetic, can lead to qualitative discrepancies between phase portraits of the resulting spatially discretized systems and the original systems. These effects can be modelled on a multidimensional integer lattice by using a dynamical system obtained by composing the transition operator of the original system with a quantizer. Such models manifest pseudorandomness which can be studied us...