Trying to Characterize Robust and Generic Dynamics

If we consider that the mathematical formulation of natural phenomena always involves simplifications of the physical laws, real significance of a model may be accorded only to those properties that are robust under perturbations. In loose terms, robustness means that some main features of a dynamical system are shared by all nearby systems. In this short article, we will explain the structure related to the presence of robust transitivity and the universal mechanisms that lead to lack of robustness. Providing a conceptual framework, the goal is to show how this approach helps to describe 'generic' dynamics in the space of all dynamical systems.