Absolutely Continuous Invariant Measures of Piecewise Linear Lorenz Maps

Yi Ming Ding, Ai Hua Fan, Jing Hu Yu

Consider piecewise linear Lorenz maps on $[0,1]$ of the following form \[ f_{a,b,c}(x)= {ll} ax+1-ac & x \in [0, c) b(x-c) & x \in (c, 1].\] We prove that $f_{a,b,c}$ admits an ab…