Generations of solvable discrete-time dynamical systems

Abstract

A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving N time-dependent variables and being as well solvable by algebraic operations (essentially by finding the N zeros of explicitly known polynomials of degree N). The dynamical systems constructed using this technique may also feature large numbers of arbitrary constants, and they need not be autonomous. The solvable character of these models allows to identify special cases with remarkable time evolutions: for instance, isochronous or asymptotically isochronous discrete-time dynamical systems. The technique is illustrated by a few examples.