For a system of linear ordinary differential equations with constant coefficients a simple proof is given that hyperbolicity is equivalent to shadowing.
@article{urn:eudml:doc:41528, title = {Shadowing for linear systems of differential equations.}, journal = {Publicacions Matem\`atiques}, volume = {37}, year = {1993}, pages = {245-253}, mrnumber = {MR1249229}, zbl = {0804.34010}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41528} }
Ombach, Jerzy. Shadowing for linear systems of differential equations.. Publicacions Matemàtiques, Tome 37 (1993) pp. 245-253. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41528/