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

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.