An open set of maps for which every point is absolutely nonshadowable

We consider a class of nonhyperbolic systems, for which there are two fixed points in an attractor having a dense trajectory; the unstable manifold of one has dimension one and the other's is two dimensional. Under the condition that there exists a direction which is more expanding than other directions, we show that such attractors are nonshadowable. Using this theorem, we prove that there is an open set of diffeomorphisms (in the $C^{r}$-topology, $r > 1$) for which every point is absolutely nonshadowable, i.e., there exists $\epsilon > 0$ such that, for every $\delta > 0$, almost every $\delta$-pseudo trajectory starting from this point is $\epsilon$-nonshadowable.