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ABSTRACT The notion of shadowable points was introduced by Morales in his recent paper (2016, Dynamical Systems). A shadowable point of a continuous map or a homeomorphism is defined to… Click to show full abstract
ABSTRACT The notion of shadowable points was introduced by Morales in his recent paper (2016, Dynamical Systems). A shadowable point of a continuous map or a homeomorphism is defined to be a point such that the shadowing lemma holds for pseudo orbits passing through the point. In this paper, as a quantitative version of the shadowable points, we study shadowable points with a given shadowing accuracy, and prove a quantitative version of Morales’ theorem in his paper above. In addition, we answer two questions on shadowable points asked in the paper.
Journal Title: Dynamical Systems
Year Published: 2017
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