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. [ABSTRACT FROM AUTHOR]