Geodesic
$C^0$ Transversality and Shadowing Properties
Informatics and Automation, Dynamical systems and optimization, Tome 256 (2007), pp. 305-319.

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Let $f$ be an Axiom A diffeomorphism of a closed smooth two-dimensional manifold. It is shown that the following statements are equivalent: (a) $f$ satisfies the $C^0$ transversality condition, (b) $f$ has the shadowing property, and (c) $f$ has the inverse shadowing property with respect to a class of continuous methods. 
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S. Yu. Pilyugin; K. Sakai. $C^0$ Transversality and Shadowing Properties. Informatics and Automation, Dynamical systems and optimization, Tome 256 (2007), pp. 305-319. http://geodesic.mathdoc.fr/item/TRSPY_2007_256_a16/

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