Geodesic
General hyperbolicity conditions for set-valued mappings
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 172-186

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We give a definition of hyperbolicity for dynamical systems generated by set-valued mappings of general form in terms of local selectors. It is shown that a system hyperbolic in this sense has the shadowing and inverse shadowing properties. It is also shown that the hyperbolicity property holds true for a certain class of set-valued mappings in which images of points are convex polytopes. Bibl. – 13 titles. 
@article{ZNSL_2009_372_a16,
     author = {S. Yu. Pilyugin and J. Rieger},
     title = {General hyperbolicity conditions for set-valued mappings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {172--186},
     publisher = {mathdoc},
     volume = {372},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a16/}
}
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S. Yu. Pilyugin; J. Rieger. General hyperbolicity conditions for set-valued mappings. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 172-186. http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a16/