Geodesic
$C^0$ Transversality and Shadowing Properties
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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. 
@article{TM_2007_256_a16,
     author = {S. Yu. Pilyugin and K. Sakai},
     title = {$C^0$ {Transversality} and {Shadowing} {Properties}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {305--319},
     publisher = {mathdoc},
     volume = {256},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2007_256_a16/}
}
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S. Yu. Pilyugin; K. Sakai. $C^0$ Transversality and Shadowing Properties. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and optimization, Tome 256 (2007), pp. 305-319. http://geodesic.mathdoc.fr/item/TM_2007_256_a16/