On the genericity of the shadowing property for conservative   homeomorphisms
  We prove the genericity of the shadowing and periodic shadowing properties for both conservative and dissipative homeomorphisms on a compact connected manifold. Our proof is valid for topological manifolds and still holds in the dissipative case. As a consequence of this result, we establish the genericity of the specification property, the average shadowing property and the asymptotic average shadowing property in the conservative case. 
Pierre-Antoine Guih\'eneuf and Thibault Lefeuvre
math.DS