  We consider some local entropy properties of dynamical systems under the
assumption of shadowing. In the first part, we give necessary and sufficient
conditions for shadowable points to be certain entropy points. In the second
part, we give some necessary and sufficient conditions for (non)
h-expansiveness under the assumption of shadowing and chain transitivity; and
use the result to present a counter-example for a question raised by Artigue et
al. [Proc. Amer. Math. Soc. 150 (2022), 3369-3378].
