Conditional mixing conjecture for Lozi maps

Let $f(x,y)=(1+y-a|x|,bx)$ be a Lozi map with parameters $(a,b)$ in the chaotic regime described above, and let $\rho(\cdot\mid x_0)$ denote the conditional SRB measure on the level curve $x=x_0$. Conditional mixing conjecture for Lozi maps. For generic Lozi parameters $(a,b)$ and Lebesgue-almost all $x_0\in\mathbb{R}$, the Lozi map has conditional mixing with respect to the level curve $x=x_0$; that is, the measures $\rho(\cdot\mid x_0)$ pushed forward under $f$ converge back to the full SRB measure $\rho$ at an exponential rate. The conjecture proposes a generalization of the conditional-mixing results proved for baker's maps to the less structured, piecewise hyperbolic Lozi maps; the stated genericity and exponential convergence remain unproved.