  Recently, Buzzi showed in the compact case that the entropy map
$f\rightarrow$ $h_{top}(f)$ is lower semi-continuous for all piecewise affine
surface homeomorphisms. We prove that topological entropy for the Lozi maps can
jump from zero to a value above 0.1203 as one crosses a particular parameter
and hence it is not upper semi-continuous in general. Moreover, our results can
be extended to a small neighborhood of this parameter showing the jump in the
entropy occurs along a line segment in the parameter space.

Dynamical Systems;Chaotic Dynamics