In the third flow region, behind the stator there is uniform axial steady flow and zero swirl with downstream-propagating acoustic and vorticity perturbations.
Moreover, we obtain sharp spectral stability results for deterministic and random perturbations.
Unlike the smooth expanding maps treated just above, such maps are in general not structurally or measure-theoretically stable with respect to deterministic perturbations.
We now describe the sequence of perturbations that produces the desired metric.
We are far from understanding how these abnormalities co-operate during tumourigenesis and how such perturbations in cell cycle control could be used clinically.
The situation in which we apply bump perturbations will often be of the following type.
An attractor state is insensitive to (small) perturbations.
Our stability analysis, for perturbations of localized solutions, typically leads to singularly perturbed eigenvalue problems with spatially inhomogeneous coefficients that are difficult to study analytically.
