Preprint A278/2004
There are singular hyperbolic flows without spectral decomposition

Maria Jose Pacifico | Bautista, Serafin | Morales, Carlos

**Keywords: **
spectral decomposition | singular-hyperbolic

A flow X_t is singular-hyperbolic
if its singularities are hyperbolic
and its non-wandering set is partially hyperbolic with
volume expanding central direction,
either for X_t or X_{-t}, the reverse flow.
We show that every closed 3-manifold
supports a C^\infty singular-hyperbolic flow
whose non-wandering set has dense closed orbits and is
not a union
of disjoint homoclinic classes and singularities.