The discrete butterfly

Abstract

In this paper we present and analyze a new discontinuous piecewise linear map of the plane, f(x,y)=(1-a|y|+x,bxsgn(y)), then we describe in detail the dynamical behaviour of this map, especially, a rigorous proof of chaos in this map is given, along its dynamics is presented in term of a single bifurcation parameter. Regarding to the shape of the new attractor presented in this paper, we call it: The discrete butterfly.