(Challenge) The Lozi Attractor2 Consider the piecewise linear map LA,B : R2 defined by LA,B = (1+y A|x|,Bx). Assume that 0 < B < 1,A > B +1, and 2A+B < 4. (For parts (c)-(e) it may be necessary to choose numerical values for A and B to avoid messy algebra. A = 1.7 and B = 0.5 are suitable.) (a) Prove that L has two fixed points, one of which lies in the first quadrant of the plane. Call this point p