A well-known result in the area of dynamical systems asserts that any invertible hyperbolic operator on any Banach space is structurally stable. This result was originally obtained by Hartman in 1960 for operators on finite-dimensional spaces. The general case was independently obtained by Palis and Pugh around 1968. We will exhibit a class of examples of structurally stable operators that are not hyperbolic, thereby showing that the converse of the above-mentioned result is false in general. We will also prove that an invertible operator on a Banach space is hyperbolic if and only if it is expansive and has the shadowing property. Moreover, we will show that if a structurally stable operator is expansive, then it must be uniformly expansive. Finally, we will characterize the weighted shifts on the spaces $c_{0}(\mathbb{Z})$ and $\ell _{p}(\mathbb{Z})$ ( $1\leq p<\infty$ ) that satisfy the shadowing property.

Highly transparent undoped and indium doped ZnO thin films have been grown on glass substrates by using the spray pyrolysis process. Conditions of preparation have been optimized to get good quality and reproducible films with required properties. Polycrystalline films with an hexagonal Wurtzite-type structure were easily obtained under the optimum spraying conditions. Both of samples have shown high transmission coefficient in the visible and infrared wavelength range with sharp absorption edge around 380 nm which closely corresponds to the intrinsic band-gap of ZnO (3.2 eV). Orientation and crystallites size were remarkably modified by deposition temperature and indium doping.