A (short) survey on dominated splittings

In the last two decades, dominated splitting has been playing a central role in the theory of global dynamics, particularly understanding non hyperbolic dynamics and extending many results known for hyperbolic theory. We present here this notion, its basic properties, a brief account on its relationship with global dynamics, and give some important results on its dynamical consequences and shed some light on how it can fail to be hyperbolic and related problems. The complete understanding of these results and problems will represent a definite step to have a comprehensive picture of global dynamics.