Analytical Solution of the Chaotic Piecewise Linear Planar Map

Abstract

Generally, there is no analytical method to calculate the chaotic solution of a dynamical system. In this paper, a simple proof of the existence of analytical solution in a discontinuous 2D discrete time piecewise chaotic map is reported, i.e., we show that a map that has a simple analytical solution can also have a chaotic attractor by the use of the classical definition of the Jordan canonical form defined for matrices available in most kinds of literature on linear algebra.