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We prove that the completely irregular set is Baire generic for everynon-uniquely ergodic transitive continuous map which satisfies the shadowingproperty and acts on a compact metric space without isolated points. We alsoshow that, under the previous assumptions, the orbit of any completelyirregular point is dense. Afterwards, we analyze the connection betweentransitivity and the shadowing property, draw a few consequences of their jointaction within the family of expansive homeomorphisms, and discuss severalexamples to test the scope of our results.

On the completely irregular set for systems with the shadowing property