A singular-hyperbolic set for flows
is a partially hyperbolic
set with singularities (hyperbolic ones) and volume expanding central direction .
properties of hyperbolic systems have been conjectured
for the singular-hyperbolic sets [8, p. 335].
Related to these conjectures we shall prove the
existence of transitive, isolated,
singular-hyperbolic set without periodic orbits
on any $3$-manifold.
In particular, the periodic orbits are not necessarily
dense in the limit set of a
isolated singular-hyperbolic set.