  We consider the dynamics of `nonlinear tent maps': piecewise smooth unimodal
maps with nowhere vanishing derivative. We show that if a nonlinear tent map
$f$ is not infinitely renormalizable, then all its periodic orbits of
sufficiently high period are hyperbolic repelling. If additionally all periodic
orbits of $f$ are hyperbolic, then $f$ has at most finitely many periodic
attractors and there is a hyperbolic expansion outside the basins of these
periodic attractors. In particular, if a nonlinear tent map $f$ is not
infinitely renormalizable and all its periodic orbits are hyperbolic repelling,
then some iterate of $f$ is expanding. In this case, $f$ admits an absolutely
continuous invariant probability measure.

Dynamical Systems