Abstract
We prove that shadowing (the pseudo-orbit tracing property),periodic shadowing (tracing periodic pseudo-orbitswith periodic real trajectories),and inverse shadowing with respect to certain families of methods(tracing all real orbits of the systemwith pseudo-orbits generated by arbitrary methods from these families)are all generic in the class of continuous mapsand in the class of continuous onto maps on compact topological manifolds(with or without boundary) that admit a decomposition(including triangulable manifolds and manifolds with handlebody).
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