EXPLICITLY SOLVABLE SYSTEMS OF FIRST-ORDER DIFFERENCE EQUATIONS WITH HOMOGENEOUS POLYNOMIAL RIGHT-HAND SIDES

Abstract

In this short paper we identify special systems of (an arbitrary number) N of first-order Difference Equations with nonlinear homogeneous polynomials of arbitrary degree M in their right-hand sides, which feature very simple explicit solutions. A novelty of these findings is to consider special systems characterized by constraints involving both their parameters and their initial data.