Weakly Nonlinear Perceptrons
The character of the dynamics of linear both flows and cascades is well investigated. It is known, among others, that the cascades generated by a linear flow preserve regular dynamics of the flow. In particular, the problems connected with topological conjugacy and shadowing properties are resolved. The regular dynamics of linear dynamical systems is preserved if they are weakly distorted - so called weakly nonlinear dynamical systems. This is formulated strictly in Grobman and Hartman theorems and Fečkan Theorem - see Sect. 5.6.