Resumen de Shadowing Property and Invariant Measures Having Full Supports

Kazumine Moriyasu, Kazuhiro Sakai, Naoya Sumi

• We consider the shadowing property from the measure theoretical view point. Let f be a homeomorphism of a compact metric space. Then f has the shadowing property on the chain recurrent set if and only if there exists a shadowable f-invariant measure having full support. Suppose that f does not have the shadowing property. Then, if there exists a f-invariant measure having full support, then, generically, every f-invariant measure is not shadowable.