A remark on the topological stability of symplectomorphisms

We prove that the C1 interior of the set of all topologically stable C1 symplectomorphisms is contained in the set of Anosov symplectomorphisms.Comment: 4 page

Topological stability for conservative systems

We prove that the C1-interior of the set of all topologically stable C1-incompressible flows is contained in the set of Anosov incompressible flows. Moreover, we obtain an analogous result for the discrete-time case.Comment: 8 page