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It is ``folklore'' that the solution to a set reachability problem for adynamical system is only noncomputable because of non-robustness reasons. Arobustness condition that can be imposed on a dynamical system is therequirement of the chain reachable set to equal the closure of the reachableset. We claim that this condition necessarily imposes strong conditions on thedynamical system. For instance, if the space is connected and compact and weare computing a chain reachable robust single valued function $f$ then $f$cannot have an unstable fixed point or unstable periodic cycle.

A Necessary Condition on Chain Reachable Robustness of Dynamical Systems