Entropy points of continuous maps with the sensitivity and the shadowing property

摘要

We give some sufficient conditions that a point can be approximated by an entropy point in terms of the sensitivity and the shadowing property. More precisely, we prove that for a continuous self-map f of a compact metric space X and a closed f-invariant subset S subset of X, if eventually sensitive points of f vertical bar s are dense in S, then any point of S can be approximated by an entropy point with an accuracy corresponding to that of the shadowing. Moreover, its homeomorphisms version and two corollaries are proved. (C) 2016 Elsevier B.V. All rights reserved.